Birne Binegar: Okay.
Birne Binegar: assigned to is do.
Birne Binegar: I have not yet posted.
Birne Binegar: Three all three that I get it back.
Birne Binegar: That will be a week from today and I mentioned it getting towards the end of the material that would be covered, on the first midterm.
Birne Binegar: that's nice to have like until maybe often.
Birne Binegar: By the end of this, but then you have a problem to on in the area I don't think the first midterm could occur at the very.
Birne Binegar: end of next week, so I think more likely will be the all anyway.
Birne Binegar: Because I think.
Birne Binegar: So we'll have a discussion this week exactly when the first mission will occur, but I think it's maybe likely not next week, but the following.
Birne Binegar: I suspect, when I pull the class people tend to choose the latter can be rather than the former date but, of course, if you have other hand, the beginning.
Birne Binegar: i'll take that into account.
Birne Binegar: lots of people taking two exams on the same day I guess the.
Birne Binegar: exam to fail.
Birne Binegar: Okay, so.
Birne Binegar: What we're going to do today is we're going to.
Birne Binegar: Finish out with our method of solving linear system.
Birne Binegar: number.
Birne Binegar: One last didn't really have been covered explicit and that's how you go from the augmented matrix and reduced lunch one or two the hyper planes expression of the solution so i'll cover that today, then what i'm going to just do some temple The key thing to walk or the road.
Birne Binegar: that's easy but.
Birne Binegar: Part of the calculation, but unless you've seen it done so fun.
Birne Binegar: it's kind of visual I need to demonstrate it, but once you once you see the pattern what looking for it's pretty easy.
Birne Binegar: Okay, so be Catholic or method, and now they.
Birne Binegar: have an augmented matrix reduce was one for so remember the argument that victory encapsulates.
Birne Binegar: The data that goes into specifying your linear system so they're easier to work with it easier to manipulate augmented matrix.
Birne Binegar: You often than it is to manipulate settings equation that we operate on.
Birne Binegar: The course on villagers.
Birne Binegar: Are goal, then, is to get you on a mission and that's going to be an organization at.
Birne Binegar: Once we get that will convert back to equation in the last step is going to be stress our solution as a hyper.
Birne Binegar: Okay, so for For those of you who are coming in just now I realized that this class way along in the boondocks there's another, for example, engineering so yeah I don't want you guys coming in, like Okay, but what I did say yes.
Birne Binegar: ma'am is likely, the.
Birne Binegar: The earliest possible end of next week for more likely not two weeks from from this okay.
Birne Binegar: All right, so.
Birne Binegar: The production method is where you take a linear system of linear equations and down.
Birne Binegar: The coefficients in the numbers that appear on like and, by the way, you can follow the date them in a single week.
Birne Binegar: And then the idea, yes, you perform element you go on.
Birne Binegar: These are operating on the authentic matrix that effectively correspond to think we can do the equations don't change the solution.
Birne Binegar: The idea is the augmented matrix of the visual.
Birne Binegar: and systematically converted to the authentic what we would call the solution.
Birne Binegar: Then, once we get the on maybe Lucy.
Birne Binegar: equation, and finally.
Birne Binegar: said, as a matter I was playing city like a third.
Birne Binegar: So we pretty much covered the first use.
Birne Binegar: Case today on the black black.
Birne Binegar: don't, mind you, through your systems, your system, a.
Birne Binegar: System of linear equations you don't get converted into a matrix graphical vision.
Birne Binegar: For this, so called often.
Birne Binegar: It basically testflight all the data.
Birne Binegar: And if you have.
Birne Binegar: Roughly between these two sections of a linear.
Birne Binegar: You call us to take your matrix and reduce it to.
Birne Binegar: You real offering you change it to reduce the last month or.
Birne Binegar: So.
Birne Binegar: Very quickly.
Birne Binegar: We say a matrix using throw.
Birne Binegar: This is nice it's.
Birne Binegar: kind of upper triangular another.
Birne Binegar: Although this is a little actually a little bit weaker than grow as one for what we're required.
Birne Binegar: Is that.
Birne Binegar: You look at the matrix there can be.
Birne Binegar: There oh.
Birne Binegar: This doesn't rely on for the zeros pushed off to the.
Birne Binegar: Left and download and then you might have a non zero entry other parts of the matrix.
Birne Binegar: The key thing for matrix in real life, for the first non zero terms that a person any row.
Birne Binegar: way they appear in the in the matrix isn't that sort of downward staircase session.
Birne Binegar: Here from top tip it moving downwards and off to the right.
Birne Binegar: Now to get in reduce throw a short form.
Birne Binegar: We have two additional requirements, you want this you want the pivot.
Birne Binegar: All equal one.
Birne Binegar: And then, furthermore, if you have a premise or wrote you can have non zero entries above.
Birne Binegar: But if you have a column, that does not have pivots you could have a number here, as long as there's no tickets in this call you can have.
Birne Binegar: Numbers up in this upper right hand corner, so the way you go from religion month will reduce your question is you scale the rose to make sure the pivots are all one, and then you use the lower road to clear out entries above the above.
Birne Binegar: Okay, and the idea that the major season, reduce your lifeline for first of all, there you need to give it given day trips.
Birne Binegar: pick an arbitrary matrix there's only one reduce rational and form that corresponds to it.
Birne Binegar: And secondly, of course, these are the augmented matrix sees that would correspond to the solution of linear system that is what I mean by that is that when I write down the equations.
Birne Binegar: For be a matrix report on form, it appears to be the best expression for the solution of the actual linear system.
Birne Binegar: Okay now what i'm going to concentrate on today is how we go from a matrix and reduce your actual one or two.
Birne Binegar: So.
Birne Binegar: Again with.
Birne Binegar: These ideas of what fixed variable art and what three variables arms Lucy you see only solve systems of equations and we have fewer equations, then we have known we don't have enough conditions to specify the variable uniquely and, in general, you're going to have info you any solution.
Birne Binegar: So how do we talk about the size of this.
Birne Binegar: Well, it basically considers dimension, rather than number of points it's in its own pizza and.
Birne Binegar: That you can.
Birne Binegar: be determined by the number of feet very.
Birne Binegar: Well, I mean.
Birne Binegar: We want to pop up one equation, and two of them.
Birne Binegar: I didn't rewrite the equation by solving for why what you would do in high school and what this is telling me to it or any particular value X value of the other variables sticks.
Birne Binegar: don't think of access, being the free variable and the wise, secondly secondary dixter it will this determined by the value of three variables solution.
Birne Binegar: So what are my equation this way I saw one variable in terms of others, all this, a big variable in this reader and, of course, for this equation, I could have also chosen to solve for X, rather than why.
Birne Binegar: I just interpret it in this instance type of ticket X is terrible because it can be specified.
Birne Binegar: Once I fix the value a lot why the free variable equation X sister.
Birne Binegar: Okay, so.
Birne Binegar: When we're labeling variables by letters, maybe we can order them right now.
Birne Binegar: But we're typically what i'm doing i'm talking about variables i'm using such.
Birne Binegar: Lead seems very.
Birne Binegar: and
Birne Binegar: I think now that said in a previous slide is actually why and a toy, which are regarding the free variable in which I regarded as a fixed variable but on our own production company is going to tell us, naturally, which variables are read which variable.
Birne Binegar: our faith in our solution just a simple rule.
Birne Binegar: it's all a bit of a treat each call on the part where respond to the variable will say to a variable in the corresponding to be I call kind of be a fixed variable if that I column contains a pit.
Birne Binegar: So, for example here.
Birne Binegar: Here we have a pivot in 1234 times in this fifth call, we have a kid that wouldn't be the fifth variable X five to be regarded as a fixed variable.
Birne Binegar: it's possible to have calls in your augmented matrix that does not contain.
Birne Binegar: Those variables are going to be regarded as the corresponding variables i'm going to leave our history.
Birne Binegar: We can even.
Birne Binegar: Oh here's another matrix and reduce your question one.
Birne Binegar: Where.
Birne Binegar: you're here in here.
Birne Binegar: For Tommy coefficient side of this argument and.
Birne Binegar: And what I.
Birne Binegar: use, for this is that because homes one, three and five in the pits i'm going to interpret X one extreme as far as fixed.
Birne Binegar: or no pivots in a second and for call i'm going to interpret those two variables X force rigor.
Birne Binegar: And then, what I do.
Birne Binegar: is well I can convert this augmented matrix into equations one times X one plus two times two zero context three minus X 405 to five people want that how about that first equation several I I get to our equation to our roadmap.
Birne Binegar: Now, is where we apply our interpretation of variables is being fixed or free.
Birne Binegar: Jeremiah krieger or my picture right online has a pivot but it's fit home three has a fit so X 365 as a.
Birne Binegar: gorgeous that what i'm going to do.
Birne Binegar: Something to move the printer hold.
Birne Binegar: The the asset side of the equation.
Birne Binegar: And then, what I end up with is an expression for the variables in terms of the free variable, so this is this happens really naturally soon as you get an augmented matrix.
Birne Binegar: With you also get the interpretation of the variable that either the.
Birne Binegar: Corresponding on it for free variables work if they don't have it and we follow once we write down the equations if you just Google, the three variables over to the right hand side and then halfway you see the fixed variable are determined by breeder yeah.
Birne Binegar: What are we.
Birne Binegar: Are are.
To.
Birne Binegar: Each one.
Birne Binegar: So i've got remote now in this process, the road.
Birne Binegar: Once you get it in.
Birne Binegar: The position of it doesn't change any Burke actually did one for you, we scale.
Birne Binegar: Without change the positioning bakery or you clear out about it.
Birne Binegar: Later so i'm back when you get to grow, as you can tell how many three variables solution because.
Birne Binegar: we're not going to change the position you see on the call.
Birne Binegar: yeah it's crazy.
Birne Binegar: um yeah sorry, this is an extra point was call for.
Birne Binegar: This variable in terms of the premier yeah.
Birne Binegar: We want to.
Birne Binegar: work.
Birne Binegar: On the next step Okay, so the next step, so what we're working towards is a higher plane expression that's.
Birne Binegar: All I got so far is the Roi that she has to simplify the equations as much as we can simplify the equation that regard these equations that equation solution.
Birne Binegar: that's a little bit more explicit when we pick a subset of a variable and are able to express them uniquely rebrand.
Birne Binegar: Well that's it for doing high school out this all up that best presentation, you have a solution, but we're looking forward to you as a teacher as well, so our process is not going to be pleased misty rather gonna be i'm gonna.
Birne Binegar: make this a loop.
Birne Binegar: doctors who coordinates or who components that a funny position we're getting expressed as point.
Birne Binegar: But it's pretty simple to do.
Birne Binegar: It.
Birne Binegar: The first thing you do.
Birne Binegar: Is you write down as technical solution, so this guy is both here's here's where it is not component before we actually apply evaluation, but we call it X one X three x five of all experience what i'm gonna do i'm gonna be a variable is general.
Birne Binegar: ID solution.
Birne Binegar: The equations for the big variables in terms of the prepared and then after that clearly dependent only on the ground, you can see that, by changing the number for various factors.
Birne Binegar: Right, though.
Birne Binegar: The fire hydroplane yet, but really easy to extract a higher plane from what we do is we take that solution that they're rough some people we call it a parametric pressure on the solution X two X four parameters which is very generate a whole solution said.
Birne Binegar: Well, what we do is we expand these factors like this in terms of the three parameters So the first thing I do is I look at each component and I broke it up into conscious term in terms of one of the three very go, so this first component there for one.
Birne Binegar: distributor minus two.
Birne Binegar: minus two because it's coefficient is on do and then minus four.
Birne Binegar: and similarly X to it only appears.
Birne Binegar: There, so I guess this vector consists of all the constant term yeah paid out of each component of this high dimensional.
Birne Binegar: conflict.
Birne Binegar: For those in a single factor this next factor it corresponds to the terms, that is all X two I got one from here, and one from here, but the last three components them you kind of X to at all, but I just had zeros there.
Birne Binegar: And then I have another variable X for on crap all his appearances, the various components of it.
Birne Binegar: And it appears three slots and I just put it there and then finally.
Birne Binegar: Is that these two terms of common factors each component X two X for our fall out of contact.
Birne Binegar: record of doing this is it now, I actually display the solution vector as a point on a two dimensional either one or two dimensional plane here's a starting point that I have some parameter one direction, and another parameter comes in other.
Birne Binegar: Words the solution.
Birne Binegar: ask for a higher starting point and two directions for which we stray from that starting point they generate a whole flat surface.
Birne Binegar: and
Birne Binegar: The C drive action I just for this concept vector my way.
Birne Binegar: back and being able to I think of that one yeah that could be too late.
Birne Binegar: And i'm impressed 30 X two X or three parameters in my solution in the same way I interpret these parameters human he do to generate like.
Birne Binegar: A very the numbers money to the.
Birne Binegar: library X two X or I can review our solutions.
Birne Binegar: Okay, so it's it's pretty easy and straightforward.
Birne Binegar: Half from the augmented matrix and reduced form to this hyper planes version of this illusion.
Birne Binegar: This lineup you that's how we want to see this solution presented thing around.
Birne Binegar: Alright, so we do that for me.
Birne Binegar: Just the screen a little bit.
Birne Binegar: So the first thing we do.
Birne Binegar: Once we have an automated victory in it's ideal for us, or we look at it and.
Birne Binegar: Finish.
Birne Binegar: Variable that be fixed or three variables according to whether a calm and corresponds to the variable contains a pivot or not.
Birne Binegar: And then we write down the equations.
Birne Binegar: Moving the free variables, to the right hand side that gives us equations that expresses the fixed variable directly in terms of the preview.
Birne Binegar: next step is for write down the general solution factor, where.
Birne Binegar: For the fixed variable will be placed in service impression save X one X, one can be expressed in terms of the free variable rather than putting X one in the solution vector we use the expression for X one in terms of the revert.
Birne Binegar: And then the last step is to expand that solution director in terms of the three parameters and then you'll get a high.
Birne Binegar: Okay, so that's about that, and what i'm going to do for the rest of today's lecture is just work through example so we'll get you the last part where we go.
Birne Binegar: Down the solution.
Birne Binegar: Good.
Birne Binegar: Any handle.
Birne Binegar: Okay, so in this example, let me show you this, what happens when your equation cancer in redundancies.
Birne Binegar: When I first began to talk about linear equations I said well normally the size of your solution set that dimension of your solution set is the number of equations.
Birne Binegar: subtracted from the number of.
Birne Binegar: A number of variables and every time you impose an equation effectively you fixed one and variables in terms of the other.
Birne Binegar: So here we have three boys and three are down, I should expect naive solution set of dimension zero because I have very quaint town should be possible my easily to fix the variable equal.
Birne Binegar: However.
Birne Binegar: What we'll see in this example is that.
Birne Binegar: We have more than one solution to this system of equation and that's because somewhere in the system of equations some redundancy it's not obvious or or growing up your process to actually expose that.
Birne Binegar: let's go ahead and calculate a solution to that equation.
Birne Binegar: room we offer the equation of course on augment your co video one book one book one and number of writing in.
Birne Binegar: a row, and the other roads are simply.
Birne Binegar: lake.
Birne Binegar: And then.
Birne Binegar: We start with our production process.
Birne Binegar: So let's look at this.
Birne Binegar: is often a major if not enrolled on remember our first goal of role reaction to get the matrix in rotation.
Birne Binegar: But the pivots occurring downwards directives that are happening to this original matrix because you have it is the first call each of the three rows are going to get rid of this guy this guy we just hit it off propofol and we want these guys, to be replaced by zero thesis.
Birne Binegar: enrollment form up to the second row.
Birne Binegar: Alright So how do I get rid of these two answers well I use the first row effectively to remove the leading term in the second row in in the third of all I have to do it for this guy is the second row by it's different first one and okay.
Birne Binegar: We.
Birne Binegar: All have one minus one.
Birne Binegar: Negative one minus one to 1100 like us to negative, but you just walk across the road to figure out what that row offering.
Birne Binegar: And suddenly you get rid of this free underneath the pivot and the courage to do that, I can subtract three times that.
Birne Binegar: I need to multiply by three the first row so that I get a cancellation.
Birne Binegar: And it'll be three minus three times 101 minus three times, one is negative, two, three minus 3.10 or minus three times two is going to be.
Birne Binegar: Negative station or four minus two okay so.
Birne Binegar: i've got the matrix in a row so much for that lead up to the second row now, but I have another pitted sitting directly below another bit, but I want to get rid of this guy so that's easy to get rid of all the use of track the third row on the second row and i'll get back all the terms.
Birne Binegar: So to track feel free to and use that replace the idea of zeros on.
Birne Binegar: So what happened here.
Birne Binegar: He.
Birne Binegar: He can he help you grow oranges, is just taking a more thorough analysis to another what I meant to do is combine these rows in such a way that the road at zero will feel that way that these are the way of the equation so, then I got the trivial shiro is zero.
Birne Binegar: Well, that happens because.
Birne Binegar: I suppose you have equation one plus.
Birne Binegar: Two plus.
Birne Binegar: equation three equals zero well, that means that equation, they.
Birne Binegar: can be expressed as.
Birne Binegar: A linear combination of the.
Birne Binegar: Other two equations to solve that these equations are not independent that they can sound the 000 that's how you do.
Birne Binegar: That, in fact, one equation and yeah depends on the other two requirements and there was a redundancy and it's been exposed by looking for correctly typically all are very.
Birne Binegar: Naturally.
Birne Binegar: OK so.
Birne Binegar: The redundancy have shown itself, I don't exactly know what linear combination of the three.
Birne Binegar: Producers zero.
Birne Binegar: But i'm not really concerned with that, and now we use a system of equations and three unknown so effectively assistant.
Birne Binegar: And that's.
Birne Binegar: The principle point of getting to run when you pitch this day you effectively eliminating all redundancies in the equation, but there's still more work to do before you actually get to the solution.
Birne Binegar: Right now, so next up we've got the row so one for the pivots are going to live or they're always going to live the rest of the calculation.
Birne Binegar: augmented matrix is not yet in simplest form one row reduce further this time we'll try to make 51 and we'll try it around entries that live above.
Birne Binegar: The little pivot already built cleared out all the entries.
Birne Binegar: Right, so you get that pivot equal one I simply by.
Birne Binegar: The second row by mind to.
Birne Binegar: And then I get a matrix that.
Birne Binegar: Is two thirds of the way we use your phone for a final step is to get rid of this.
Birne Binegar: entry is sitting about it in the second row.
and
Birne Binegar: I simply adding multiple seven wrote in the first row that will clear out that entry but subtract the seven from the first Robin I use that to replace the first row.
Birne Binegar: And that produces the matrix and reduce relational i'm.
Birne Binegar: Good.
Birne Binegar: steak steak we've now got you i've been making for solution.
Birne Binegar: That is our solutions that express it as a higher.
Birne Binegar: start with for augmented matrix.
Birne Binegar: screen a little get again.
Birne Binegar: Alright, so.
Birne Binegar: At 123 years they were on the call.
Birne Binegar: As one corresponds to call it X.
Birne Binegar: And X two is also.
Birne Binegar: That home for funny that you also could be.
Birne Binegar: But the third call it has a knock your entry but it's not.
Birne Binegar: going to be my fear.
Birne Binegar: Alright, so let's let's proceed and.
Birne Binegar: write down the equations corresponding the augment.
Birne Binegar: And then.
Birne Binegar: simplify the equation your coefficients variable disappear and then.
Birne Binegar: The equations of the solution, but at this stage, I have not yet in August when you're free variable.
Birne Binegar: Pay that explicit move the free variable as predicted by the organization called move them to the right hand side.
Birne Binegar: So from this.
Birne Binegar: s3 turned out to be the only three variables i'll move it to the right hand side now each of the fixed variable breath either return for Austin or in terms of the content in the rear.
Birne Binegar: Good.
Birne Binegar: All the end.
Birne Binegar: There was a generic solution back there when I supposed to be for the fixed variable in terms of the free or Oh, I get it after.
Birne Binegar: You pass on green vertical and the last step is to simply make this better and expanded in terms of the freegard well I have.
Birne Binegar: A better one one and they're both positive last year term, and then there are terms proportional X three x minus one first opponent, and one in the third quarter, you see it.
Birne Binegar: End about.
Birne Binegar: Why that then we all.
Birne Binegar: Is.
Birne Binegar: An expression for the solution.
Birne Binegar: Sorry didn't really show up but i'm the father hey all slide unfortunately what's your favorite, this is an expression.
Birne Binegar: Well, actually a lot because there's only a single vector.
Birne Binegar: You want.
Birne Binegar: me to over.
Birne Binegar: The entire real life experience alone.
Birne Binegar: alone, so this is behind.
Birne Binegar: On that contains all the solution to the original video system.
Birne Binegar: Okay that's the man.
Birne Binegar: So just do some more examples here and see if there any question.
Birne Binegar: yeah.
Birne Binegar: I got.
Birne Binegar: It.
Birne Binegar: Alright, so let's go back to the beginning so well at least the authentic venture.
Birne Binegar: So here i'm just going to decide whether what variables login part is free space of three variables, are the ones that don't appear, this is of course buying all it's all the extra year of just let's just remember X rays, are prepared.
Birne Binegar: And then.
Birne Binegar: The other two variables, where we fit in the palm those are going to be.
Birne Binegar: Alright, so now just go ahead and write down the equations but the next step is to reinterpret X three now the free variable so put it on the other side of the equation.
Birne Binegar: And now you see my picture it'll have any friends either.
Birne Binegar: Things that don't depend on any variable or in terms of the freedom.
Birne Binegar: Alright, so what I have no expression for X one name a few but I don't really have the equation for the free variable X Ray.
Birne Binegar: So I write down solution vector I can substitute for X one I can substitute for X two.
Birne Binegar: X two is Jesse one and X Ray is free or leave it.
Birne Binegar: And now i've got my solution every factor, and the solution can be present from the free variable X three and then the last step simply take this better.
Birne Binegar: Experience expanded in terms of rebrand the cost of the term, the term you can only one on three grand or.
Birne Binegar: hey.
Birne Binegar: All right, so.
Birne Binegar: yeah we're.
Changing but.
Birne Binegar: yeah.
Birne Binegar: So.
Birne Binegar: If you have a starting point and then you stray from that starting point, one of the greatest Russian but how far you can extend that be well I read it this way, you can on how how long this is going to depend on pine tree right.
Birne Binegar: When you scale life after basically you can change it later.
Birne Binegar: So what I need.
Birne Binegar: is consistent, all the actors that start at this one and head off in this particular direction is.
Birne Binegar: Not black blackboard like a pain point and I go a certain distance in one direction, in a certain distance the other but I reach other points and the blackboard like very nice.
Birne Binegar: So let me see if I draw so this point here, it would.
Birne Binegar: correspond, I guess, I want to draw.
Birne Binegar: A parallel.
Birne Binegar: Here alright so on this side here is perfect day that are parallel to that direction, and this side here is perpendicular to this direction, so I taking him home it's linear combination this factor was the faster it's going to produce the getting better.
Birne Binegar: So it's a way of.
Birne Binegar: Actually, using Cartesian coordinate.
Birne Binegar: plane over can line up perfectly, but it was still generating fun.
Birne Binegar: yeah it's all it's all mine because there's only one free for our there's only one direction straight initial charge.
Birne Binegar: Okay.
Birne Binegar: Alright, so.
Birne Binegar: let's do another.
Birne Binegar: Another problem solving says large systems of equations and sometimes a contradiction is not be on.
Birne Binegar: And what color rubber ducky process after you both did.
Birne Binegar: So in this example i'm deliver a setting up.
Birne Binegar: A set of replace it with their internal contradiction see that contradiction.
Birne Binegar: Let me take the first equation, so I get the second equation subtract the first equation prime and then I get well.
Birne Binegar: These two questions I get the right hand side.
Birne Binegar: But what happened on the right, if I get one cool so that.
Birne Binegar: These two equations produce an equation that contradicts the 30 foot, so there is a contradiction in here in the studio system, it can.
Birne Binegar: Be.
Birne Binegar: For Marxist if you're looking for.
Birne Binegar: One of the big achievements of the production process it finds them for you, it will tell you very early on whether or not the solution.
Birne Binegar: linear system even have a solution.
Birne Binegar: Alright, so.
Birne Binegar: i'll show you how this works.
Birne Binegar: On.
Birne Binegar: Arizona.
Birne Binegar: here's the original linear system on the slide i've gone ahead and i've written down the corresponding augmenting be.
Birne Binegar: Well, by our procedure for solving a linear system of this augmented matrix.
Birne Binegar: Little the first row told us the first row to eliminate.
Birne Binegar: This entry in the second row.
Birne Binegar: After this, and now now I have.
Birne Binegar: attended hello, is it clear out this entry find out, I guess the tracking turbo.
Birne Binegar: Exactly.
Birne Binegar: What will happen defaulted this.
Birne Binegar: We should stop here because.
Birne Binegar: My I did already spot.
Birne Binegar: We probably how I see.
Birne Binegar: It when you grow up reasons you're not changing the solution set i've done some element of operations i've got down to this.
Birne Binegar: Third row converted Community equation, and it says 080805 X three x equal free well you gotta wait, the left hand side you get zero everything the whole five and zero right hand side stage 3003.
Birne Binegar: Know it's a contradiction, so, in fact, when you identify contradiction.
Birne Binegar: Lately question.
Birne Binegar: For the equation in augmented matrix reviews and you end up with a road has a non zero entry in last all.
Birne Binegar: That means you can get an equation that says zero is equal to that answer on never be the contradiction, so this this day you problem stop because the risk of solution cheaters, and so it doesn't make any sense to even say five number for years because here's the solution.
Birne Binegar: So when this one, now that.
Birne Binegar: You get all zeros on the coefficient side yeah non zero numbers last fall that eases your solutions and the rest of solution to erase.
Birne Binegar: No, no.
Birne Binegar: The summary.
Birne Binegar: As you probably use a trip.
Birne Binegar: you'll be given clues as to what's going on in the region of the system of equations first of all with any time to zero here's your movie the matrix that be part of the throw it up now, but it's also telling you that your original system there was one equation at.
Birne Binegar: least one you get zero.
Birne Binegar: And so.
Birne Binegar: yeah that's going to tell you that.
Birne Binegar: Your account the size of the thing that you're 90 pounds me off, so I even take the number of variables track the number of equations that you sighs solutions that's only true wonder no redundancy.
Birne Binegar: So when zero appears it's going to be that your solution said it's actually more than you would expect, because there's fewer equations that you actually started off with.
Birne Binegar: And then, a period of years that last column that's going to mean you have continuity with a pivot appears.
Birne Binegar: Order, the arby's matrix the corresponding numbers on the right hand side you have non zero number there but zero on vision side asking a contradiction.
Birne Binegar: OK, so the road after this kind of application take care of technical.
Birne Binegar: going to take care of the natural.
Birne Binegar: So just a few.
Birne Binegar: Additional.
Birne Binegar: ways to start off this question.
Birne Binegar: right here down the automated matrix use these three elements we will approach, change your growth.
Birne Binegar: Change rose the road after spice feel it factor, and you can add multiple ones vote, you know you've got replaced with though he's only allowed three is that.
Birne Binegar: When you systematically will always take you from an arbitrary matrix which you need a useful for.
Birne Binegar: Roche long form is just for you have a ticket securing the staircase, and all this digital screen.
Birne Binegar: It does it.
Birne Binegar: yeah that's a little bit, I guess, to get in reduce offline, for he get the parents that have done one as done simply using before we still in operation, and then you need to clear out entries that syllable.
Birne Binegar: here's an edit I will be around.
Birne Binegar: And there you'll typically use these operations, I should also be bar that procedure I would you.
Birne Binegar: apply these operations is different when you're trying to get through a lot more new ideas start up in the upper left hand corner and you systematically work your way down and off to the right as you eliminate and physical appearance.
Birne Binegar: On you trying to get reduce your last month.
Birne Binegar: During the fall is the device.
Birne Binegar: So you started.
Birne Binegar: writing for us to pivot here we clear out the entries the bottom there you go to the next, fire youth multiples of this road they flew out entries in the road.
Birne Binegar: He says like this, this party started the other wonder you work your way down lower right at this stage in your life Lord mighty one you sort of work, your way up and.
Birne Binegar: So.
Birne Binegar: Then.
Birne Binegar: When you reach you for the goal, that is, that is to actually.
Birne Binegar: write the solution as a hyper plane up this is important, for example, what I usually do something like this on.
Birne Binegar: This first column doesn't have any entries.
Birne Binegar: That big more the forest flying variable X one know either X one is going to be preparing all the solution because there's no pivot in all so just because you have all zeros here don't forget about X one.
Birne Binegar: It doesn't even show up in any way right but.
Birne Binegar: What we what we focus on or the fixed variable Fo X two.
Birne Binegar: X three x and X files.
Birne Binegar: And he went to take the equations from this augmented matrix and move them three variables over to the right hand side I get expressions for each.
Birne Binegar: For each variable associated.
Birne Binegar: And then.
Birne Binegar: don't forget about excellent, even though didn't appear in the equation you write down solution factors stuff to the big variable and then we expand the solution better in terms of the three bears.
Birne Binegar: causative factor 321 of the components that we have for portion the next one well as my Holy Spirit.
Birne Binegar: here's one.
Birne Binegar: For you in freaking.
Birne Binegar: out.
Birne Binegar: Over the.
Birne Binegar: third component mine one on one and then six variables also free beer or.
Birne Binegar: Wine three that opponent on to third amen to that amen and want.
Birne Binegar: Alright, so I guess i'm out of time, so i'll stop here today.
Birne Binegar: What I tend to do on Wednesday lecture is move on, we do topic class if you have Problem Solving linear system will be happy to address that on Wednesday as well.