Birne Binegar: Okay, I guess, we can get started.
Birne Binegar: So, welcome to.
Birne Binegar: It so.
Birne Binegar: What i'll try to do at least in a week.
Birne Binegar: First week, they continue to provide recording, but the problem with doing doing that is i'm going to work a lot on blackboard i'm trying to arrange my laptop so it actually sees the blackboard through which camera but you're really best off to the lab.
Birne Binegar: And my discussion on the blackboard.
Birne Binegar: Any questions, by the way for someone to actually see your face.
Birne Binegar: Okay, so today what i'm going to do is i'm going to.
Birne Binegar: Well, so today i'm going to review a little bit what we covered last week.
Birne Binegar: Practice everything by saying the first few weeks of the course what i've been doing is trying to give you the calculation of tool we started talking about major cities and i've assisted the this course.
Birne Binegar: Alright, starting to be factored in i'm missing in this course, you should think of factors primarily at simply ordered list of numbers, even though they have too.
Birne Binegar: Many applications, the physical sciences, the way we'll do within this quarter list of numbers.
Birne Binegar: After the first week we went into the matrix offer.
Birne Binegar: agencies were introduced to the way of Encapsulating the information you need to specify your write down system of linear equations.
Birne Binegar: And i'll add to that a little bit, but the main point today's lecture is actually to begin to apply that stuff and the first topic we're looking at is all the current systems of equations.
Birne Binegar: They will do is will minor.
Birne Binegar: problems related to make your feet and then probably all get as far as.
Birne Binegar: giving you some intuition as to what's going on, it will try to.
Birne Binegar: give you a geometric picture of what solution look like and how you both both boy, if you change solutions.
Birne Binegar: And then I don't think and again the roadmap.
Birne Binegar: That will be a matrix techniques for folding or systems of equations.
Birne Binegar: Okay, so let's see.
Birne Binegar: So let's start with off reviewing matrix hope taken.
Birne Binegar: If you have to make up.
Birne Binegar: If you have to take.
Birne Binegar: You can offer both the other, but not all.
Birne Binegar: It number of calls in the first factor equal to the number of seconds there's a product is not going to find it as we work with it doesn't say anything, however.
Birne Binegar: When number of columns of the first factor equal number of roses.
Birne Binegar: Then we can describe that fan of eating.
Birne Binegar: fat boy entries as a new bakery the product of a be with us computed if you need to take that product.
Birne Binegar: roadmap first column a and column vector second.
Birne Binegar: This issue here is Gary vee that when you interpret the road that is ordered list of numbers, it has exactly the same number on as what you would.
Birne Binegar: call that he ordered.
Birne Binegar: up a product that has to take action.
Birne Binegar: On.
Birne Binegar: That product.
Birne Binegar: He.
Birne Binegar: Do.
Birne Binegar: w equals.
Birne Binegar: Zero that's the fine.
Birne Binegar: Well, be one minus point.
Birne Binegar: Zero what is the essential to the formula for that product it the fact that we're comparing well as offline similar components exactly yeah and then something about if this this doctor was three dimensional rather than two dimensional then dot five, with no longer.
Birne Binegar: So, because of that product required to take.
Birne Binegar: A product to get through.
Birne Binegar: This condition here just guaranteed your deposit.
Birne Binegar: The.
Birne Binegar: Road all the great individual entry of the product pages.
Birne Binegar: let's.
Birne Binegar: suppose I want to apply.
Birne Binegar: 21000 I.
Birne Binegar: made 3211101 alright so.
Birne Binegar: The key thing to check here, to see if this is even define is notice that this matrix has three room.
Birne Binegar: and recall the matrix on the right here has three rows.
Birne Binegar: and
Birne Binegar: columns and you can't you have this match.
Birne Binegar: Number of columns the first factor equal number of rows of the second factor, you are going to have a matrix product.
Birne Binegar: And back from the outer limits, you can tell it.
Birne Binegar: that's the result of both find these two pages together it's going to produce.
Birne Binegar: A matrix to rose can call why because I have two roads to choose from here.
Birne Binegar: And I have to call you all care, I can take that product of this rope this call to take down this road, this home, and I take the second row column, and has done something wrong exactly calm down i've exhausted all my rows and columns.
Birne Binegar: Exactly to produce the product.
Birne Binegar: To growth.
Birne Binegar: And exactly two columns in the product, but I have to call them off with.
Birne Binegar: The condition on there but they just have to match refer he's got product.
Birne Binegar: Which computer.
Birne Binegar: Because this guy is the one one plot.
Birne Binegar: I need to take the first row is first factor to take it starts with the first column stuff.
Birne Binegar: That was in two times two, which is for that I hope to the second one times, one is one.
Birne Binegar: And then 000 so what i've done is I quickly computed the the one one component of the product that the.
Birne Binegar: Computer yes run out of space they are looking at the races for well.
Birne Binegar: You know, let me run up to.
Birne Binegar: 410 that's in the one one spot in the one to slot first row second call, I take the first road again, but now I take it stop product second call.
Birne Binegar: Oh look like it too.
Birne Binegar: one.
Birne Binegar: zero times, one is.
Birne Binegar: Alright, so that's the one, two and three there'll be a entry, the second grow in first call.
Birne Binegar: Here we get get it, for now, then the tour in the second row well you wrote here started with a product that will use the first call to get the two one entry two times zero is zero minus one times, one is minus one and 00.
Birne Binegar: And now we're down to the last row last call.
Birne Binegar: The zero.
Birne Binegar: minus one of.
Birne Binegar: All the various calculation is to do the sun's until we get by.
Birne Binegar: Three minus one.
Birne Binegar: So the result of 4.2 by two by three day three and three by two matrix is the two by two matrix with these 453 minus one minus one.
Birne Binegar: Well, I hope, you'll be able to do it tonight, but by the time you finish your homework my homework assignment to it's going to be doing a week from today.
Birne Binegar: I announced on Friday last time that we do on this coming Friday, but because I didn't get it posted until this morning i'll give you the extra time and.
Birne Binegar: What you will do that promise that God will do the agent.
Birne Binegar: What do you want to get started good at doing, most of the calculation you.
Birne Binegar: So you get that first century i'll just go well four plus one plus zero.
Birne Binegar: see that it's working fine I go to method.
Birne Binegar: Two plus one.
Birne Binegar: You can you can do this fairly quickly, however, like most of the calculations this court it's kind of tedious.
Birne Binegar: What I will try to do my homework problem, no problem is.
Birne Binegar: The entries of a matrix any real could be the square reply could be either the X squared upon but I don't.
Birne Binegar: Does the calculation that you actually perform basically boils down to this replying and Edit.
Birne Binegar: I can choose very simple numbers typically integers so that when you do have to get down to the nuts and bolts of calculating numbers out of it you're just adding and.
Birne Binegar: multiplying integers.
Birne Binegar: Not because.
Birne Binegar: Because that's the most common in your application, but rather you'll understand the calculation, and if you had or complicated number fractions appearing rather things more difficult top few please know how the algorithm works and we just.
Birne Binegar: Did you his final calculation with my number two thing.
Birne Binegar: So.
Birne Binegar: matrix.
Birne Binegar: point out.
Birne Binegar: Before you even start double play.
Birne Binegar: Together it's wise to make sure that multiplication if you find a look at that the number of rows and columns maybe breakfast and find in this study factor, because enrollment fee.
Birne Binegar: fee, then you can make sure you have this batch of the interdimensional the outer dimension for all these old yo yo you.
Birne Binegar: The dimensions of the path as product, and it is define number road, because it can be the same as number of rows of perfect and the number of calls that can be famous number of all the.
Birne Binegar: return that if you look at this formula.
Birne Binegar: This first index I indicate a rough and so, how many choices, for I have many choices for five rows.
Birne Binegar: Number how many choices, do I have to guess both Many choices for gay will not fall for be the VP so for the number, I can vary from London and Jacob very from one to pee both going to have.
Birne Binegar: To go one column is easy to invite.
Birne Binegar: All right.
Birne Binegar: um let's see I on Friday introduce Jennifer she made it very simple wanted.
Birne Binegar: To prove useful later on it's the matrix it has the same number of rows and columns and four which one this what we call the main diagonal upper left lower write all that down below you have nothing but one but different warehouse matrix only.
Birne Binegar: very special matrix.
Birne Binegar: So pinterest because it behave exactly like the number one whenever the product.
Birne Binegar: That is it what is it what does this tell.
Birne Binegar: me the same number of columns of.
Birne Binegar: A pita equals no road on the test define yourself at a time.
Birne Binegar: going to read.
Birne Binegar: The read from a previous day and, similarly, if my whole life from the right so sorry both life of a laugh.
Birne Binegar: I get that a lot is that product.
Birne Binegar: You do one of these days or two, you have to check to make sure the number of columns to the first factor equal number of the number of rows of data.
Birne Binegar: And then decide on multiple agencies other there are other things we can do it.
Birne Binegar: We have two major things that are both have the same time, they get added and the rule is for life which extradition similar entries dissimilar enters the battery I brought de Palma.
Birne Binegar: He led and trading I wrote a column a the entry and I wrote a column B, but, of course, you have many more entries you only getting.
Birne Binegar: One entry, out of a large.
Birne Binegar: scale of all the pain.
Birne Binegar: We take every country, but he hey and you can go into the fire department number Lambda that's going to be what we call a local station.
Birne Binegar: bakery what does makes a bakery birthed it into a new bakery where in the old entry at all the whole line.
Birne Binegar: number.
Birne Binegar: I pointed out because.
Birne Binegar: The first week of class when I was sort of.
Birne Binegar: What to look for you in this course, I said that.
Birne Binegar: When considering factories to import operations under understand everything in the whole scalable Asian.
Birne Binegar: And here we defined with civil.
Birne Binegar: You asked.
Birne Binegar: me.
Birne Binegar: Like every five minutes, they both looked at each other.
Birne Binegar: For this live show here is that interesting.
This.
Birne Binegar: Past Tuesday similar operation will be later about midway through is it back, we could have agencies and the elements of.
Birne Binegar: Effective they are and just was hungry, but if they get an abstract set it on which solution of additional defined in motion and feel more refined and basket allows the tree, the addition ill patient safety in a perfectly exactly the same way.
Birne Binegar: So factory and exactly all our results are better than you going to extend the general situation, a more general now making it affordable.
Birne Binegar: But we still have to add vector operations.
Birne Binegar: Right there's one other operation introduce started with nothing to you quite a while, and that is the fact that.
Birne Binegar: We did start with a matrix with n ro n calm and from that we can produce a matrix with the number of rows.
Birne Binegar: And rows and call now become.
Birne Binegar: Really, simple, all we do is take the original matrix.
Birne Binegar: and rewrite it rose as tall, so I had to one minus one zero you.
Birne Binegar: i'll take the transpose that that's super Nice.
Birne Binegar: food.
Birne Binegar: Which is going to equal well, I think that first row and our reinterpreted as a call.
Birne Binegar: It it's an ordered list of numbers that i'm now going to write, for your second row become the second call.
Birne Binegar: And so.
Birne Binegar: The transpose operation.
Birne Binegar: yeah just convert wrote in the call or.
Birne Binegar: Whatever numbers and I wrote a column, whatever that road I call them.
Birne Binegar: Now, and so I wrote a poem.
Birne Binegar: that's exactly what's happening here and what you should also know.
Birne Binegar: Is that if I take this matrix and I take it to transpose i'm practice first row as Paul.
Birne Binegar: wrote the column right third row column I get right back sorry, so one property.
Birne Binegar: You get back where you started.
Birne Binegar: And in fact there's a number.
Birne Binegar: of simple properties of this transpose operation, you would find started.
Birne Binegar: Basically doors to Asian on all this is doing some.
Birne Binegar: Steel or changing the batteries of agree on a common factor, but once that common factors and scroll down we.
Birne Binegar: transpose operation just moving the numbers around still all the people on lamb this time he.
Birne Binegar: Later transpose operation Delhi this up a little Asian.
Birne Binegar: Her.
Birne Binegar: Because transpose operation is compatible with the addition of major please.
Birne Binegar: As a team together to transpose or.
Birne Binegar: transpose that the individual on.
Birne Binegar: me.
Birne Binegar: And we'll get the same little.
Birne Binegar: tricky one, I want to work.
Birne Binegar: If you have a product that major key.
Birne Binegar: that's.
Birne Binegar: What happens, you get a matrix it's not a product.
Birne Binegar: like this rather get a product.
Birne Binegar: or something order the factory.
Birne Binegar: At trends transposes you will.
Birne Binegar: Now, be stressful to be the left hand factor started all right man.
Birne Binegar: Well that's the only tricky part about dealing with transpose operations effects products, but all it does beside the transpose operated.
Birne Binegar: versus the order.
Birne Binegar: Okay alright so.
Birne Binegar: Much was review of what transpired when we now return to the positive motivator.
Birne Binegar: How this all has the equation.
Birne Binegar: job.
Birne Binegar: Now here's a system of equations.
Birne Binegar: linear equation, because the variable X on.
Birne Binegar: The way they have here the any of the equation is a year to the first power is worth those for root of X one X one.
Birne Binegar: X one X two variable Caribbean suffer term worst thing you can do to the things you can lie to myself number is your vision your goal and.
Birne Binegar: There could be adult terms that don't involve variables will all be one be a number and move all the numbers like mentioned over writing five he.
Birne Binegar: was terminated voluntary keep them on time every simply write down the equation.
Birne Binegar: Then.
Birne Binegar: These are related to matrices as follows.
Birne Binegar: From your equation that bridges, the gap.
Birne Binegar: right there something explicit.
Birne Binegar: On each of these coefficients a particular number what we'll do is we'll identify them put them in as tangible rich, but we have any you have any question, you know that for each equation get a row of the patrons and for each variable get it going to all.
Birne Binegar: Of this system of equation in emma's house it's gonna it's called.
Birne Binegar: A it's better to be an FBI agent.
Birne Binegar: We can also collect together all the variable right the vertically, at the end by one problem and we can put the numbers one through.
Birne Binegar: What those in a single.
Birne Binegar: Vertical ready to be a column.
Birne Binegar: Point of View.
Birne Binegar: The writing of it is that fact now that we understand what makes.
Birne Binegar: These related.
Birne Binegar: A and B.
Birne Binegar: will be satisfied this equation, and, moreover, this venture.
Birne Binegar: is exactly what you return home in your system.
Birne Binegar: We do a quick demonstration of that.
Birne Binegar: We had.
Birne Binegar: One plus.
Birne Binegar: X to y minus.
Birne Binegar: X one or three.
Birne Binegar: is equal to.
Birne Binegar: What we call a two by two system.
Birne Binegar: Because there are two equations and two and now.
Birne Binegar: How the matrix formulation of this.
Birne Binegar: would be.
Birne Binegar: working.
Birne Binegar: With these okay let's grab the politician.
Birne Binegar: Two and one right coefficient of first variable to coefficient of the second variable one in the first equation.
Birne Binegar: And the second second call is more pick up a minus one and three there's a coefficient in there are variables, we have to act on.
Birne Binegar: end to end the call that you're on the right hand side.
Birne Binegar: it's going to be wanting to.
Birne Binegar: Alright, so.
Birne Binegar: This way you're not playing the equivalent to the original in your system but it's not yet clear that that's true until you actually carry out this matrix.
Birne Binegar: Two times X one.
Birne Binegar: plus one times X to.
Birne Binegar: be done one one entry in this product that I have a second row that I can take it stock product for that call i'll get minus one plus three x.
Birne Binegar: Now, if you look at the extreme side of the equation, you see, is replicating your original linear system component by component so.
Birne Binegar: What i'm doing here is i'm taking.
Birne Binegar: The organization formulating every major.
Birne Binegar: But it's essentially the same problem I can just as easily go from a matrix equation to a linear system it's like a whole new system to make up.
Birne Binegar: Our goal it's fun it's all.
Birne Binegar: on us as.
Birne Binegar: Well that's that's the perfect place to get you into the arena, but we can solve the equation quick.
Birne Binegar: Okay.
Birne Binegar: now consider.
Birne Binegar: What I.
Birne Binegar: came to the initial equation.
Birne Binegar: baby is.
Birne Binegar: What we call a system.
Birne Binegar: like this one, with any equation.
Birne Binegar: Okay.
Birne Binegar: yeah.
Birne Binegar: I am not going to be solving any linear system today not explicitly rather the purpose of today's lecture is to get you thinking about falling equation or linear algebra term.
Birne Binegar: So i'm going to step through.
Birne Binegar: The various possibilities step on.
Birne Binegar: The idea is.
Birne Binegar: visual, we have to calculate.
Birne Binegar: So.
Birne Binegar: let's start off trying to understand what it means no equation.
Birne Binegar: sort of stupid thing we don't have any equation, but we haven't put any additions on our on our I don't for free to very over the entire real line.
Birne Binegar: So if I don't have an equation my solution that definitely you are that have ordered list of like a variable maybe write a column for each of the individual component Yuri over we are says.
Birne Binegar: Well that's all possible list of numbers exactly.
Birne Binegar: So.
Birne Binegar: We don't impose any equations we start off with a solution that it's a.
Birne Binegar: Big number of variables.
Birne Binegar: Okay, no now let's do something non trivial let's try to solve a single linear equation.
Birne Binegar: So what i'm going to do here, I think the.
Birne Binegar: default should.
Birne Binegar: be wonderful and thank you all for it, rather than.
Birne Binegar: The other, but what I do if I make make.
Birne Binegar: first set of terms move them over to the other side of the equation changing their side and then i'll be left with a an xm on left hand side like buy to buy that food is not equal to isolate at Camp on stuff they're being.
Birne Binegar: Okay, so that's how you solve.
Birne Binegar: A single equation in high school but it's not showing up linear algebra.
Birne Binegar: Let me reinterpret that a little bit.
Birne Binegar: The first thing i'm going to do.
Birne Binegar: For you, my solution in.
Birne Binegar: A variable I want to see the solution as.
Birne Binegar: well.
Birne Binegar: condition, I found that that is that equation Oh, I think we played the last variable.
Birne Binegar: By this expression in terms of the first invited wonder.
Birne Binegar: Why did I write down a generic vector X one X all the parameters, but because this is to be a solution to that linear equation laughing pony express in terms of the first appointed watch.
Birne Binegar: Good, so now we have a solution expressed as a vector rather than simply isolating one component tell you what that has to be.
Birne Binegar: The next step, I do before as well.
Birne Binegar: Before the opponent depend on variable well off exactly what the leading term here in the last component it doesn't because any is very i'm going to get pulled it out of.
Birne Binegar: The single factor off and.
Birne Binegar: Then i'm gonna focus on how X.
Birne Binegar: Factor she appears the first one, it doesn't appear to be, but it does appear again we reach the last home and then it occurred coefficient minus 818 am i'll put that thing.
Birne Binegar: i'm going.
Birne Binegar: To just go out contribution.
Birne Binegar: contributions.
Birne Binegar: I keep doing that, though I reach a.
Birne Binegar: goal.
Birne Binegar: And it has a component in the next to last block and it has a component.
Birne Binegar: If I filled out for him, I said.
Birne Binegar: Look what the impact.
Birne Binegar: of my reason for splitting it apart this way is to display the vector so hyper plane.
Birne Binegar: Right.
Birne Binegar: Now.
Birne Binegar: I had on the preceding side.
Birne Binegar: Here we go.
Birne Binegar: Perfect work.
Birne Binegar: Your.
Birne Binegar: bond zero entry or proportional X one.
Birne Binegar: X one out at the scale or back and fill in the last one you'll be zero entry of all the stuff in minus one but pull this back your mind is one.
Birne Binegar: factor.
Birne Binegar: That produces.
Birne Binegar: This other thing.
Birne Binegar: But now you can actually see before playing.
Birne Binegar: remind you that a high proclaim.
Birne Binegar: Is a set of factors that we create our story taking a starting point and then.
Birne Binegar: i'll get a list of direction he wants he wants what we what we crave it fires set of factors is P zero and think of all the points we can reach us.
Birne Binegar: By.
Birne Binegar: Our internal quality mind arbitrary do it shattered shattered glass direction.
Birne Binegar: What you should notice that this solution that.
Birne Binegar: Is the factors that are impacting us for your P zero, this is a free variable so I can very good.
Birne Binegar: Very good parameters on this is the free variable illusion, I can very good yes.
Birne Binegar: Very good friend of mine in.
Birne Binegar: fact the solution, our pipeline.
Birne Binegar: Right now, so that's the picture I want you to have a time.
Birne Binegar: I think only place repairing.
Birne Binegar: The dimension of the fiber plane this variable started off with.
Birne Binegar: This Tommy direction.
Birne Binegar: Well, one last number variable.
Birne Binegar: In other words.
Birne Binegar: If you.
Birne Binegar: Have any questions at all, no restrictions on your variable you get me.
Birne Binegar: Though we quickly.
Birne Binegar: Finish you have both one equation now, it looks like the dimension that we do live one life because i'm just starting point and i'm only allowed to lead them to the point in N minus one direction, so I get a lower dimensional space of solution.
Birne Binegar: Exactly one dimension board if you reach out very.
Birne Binegar: Moral the story is you have one equation and variable solution that is going to be fit into one dimensional.
Birne Binegar: One equation three announce the solution that is going to be a two dimensional type of the bed, if you.
Birne Binegar: let's get a picture of that.
Birne Binegar: So here's an example.
Birne Binegar: i'm able.
Birne Binegar: To produce this breath.
Birne Binegar: This equation this linear equation and three good work excellent Why do I asked it to block all points by did you that satisfies the equation, and what happened returns to be on a flat surface, this is embedded in the region box.
Birne Binegar: get some pieces of paper out to represent flat surfaces.
Birne Binegar: So you can see.
Birne Binegar: Pictures of the Room three dimensional be the overall a variable.
Birne Binegar: equation, but that's going to put out the fire people laugh certain.
Birne Binegar: you're defying to play box, but you should think of it.
Birne Binegar: direction and.
Birne Binegar: interpret.
Birne Binegar: The solution set of single equation as be.
Birne Binegar: Black surfaces of dimension one less of the face of every.
Birne Binegar: album looking to equal.
Birne Binegar: And what that's going to be if you're on to equation, but this picture is trying to do is it one of these before.
Birne Binegar: The course with this thing called equations three variables.
Birne Binegar: Two dimensional solution there's another equation and it's going to have another any kind of solution.
Birne Binegar: To satisfy both equations, not only does the boy have to live on the first time I played it all day long.
Birne Binegar: So our solution says view magically are created by be intersect.
Birne Binegar: What i'm gonna do next we're going to explore what kind of.
Birne Binegar: effect yeah.
Birne Binegar: And although I will prove this now well stated at the fact that we develop our technique oh wait to see.
Birne Binegar: What every time you said is fine, because other type of plane.
Birne Binegar: have already mentioned.
Birne Binegar: i'll show you the special cases, you don't get involved, but the.
Birne Binegar: basic idea is you how.
Birne Binegar: Did you get.
Birne Binegar: Multiple apple that just a second.
Birne Binegar: Okay, so let's see here all right.
Birne Binegar: Before we do that place of course on the contradictory.
Birne Binegar: there's two equations three variables and a lot of both there, of course, buying it.
Birne Binegar: You only see one one flat surface you that's because that these two equations are equivalent.
Birne Binegar: equation, just to confirm very it's going to have exactly the same solution that maybe the first step to solving this equation, will be in a central equation.
So.
Birne Binegar: It should be added, more equation, but it doesn't necessarily solutions that's a pretty.
Birne Binegar: Traditional vote by adding a new equation, they already be by by the preceding right.
Birne Binegar: Now this is the.
Birne Binegar: equation on duty equivalent, but if you have any questions and 11.
Birne Binegar: There will be some connection between never get there just.
Birne Binegar: One of the things they forget to try.
Birne Binegar: On your system is loving relationship, how do I get upon when we have independent equation.
Birne Binegar: That actually independently.
Birne Binegar: And then.
Birne Binegar: Another problem if we get to the contradictory equation.
Birne Binegar: Here we have you have a funny little girl.
Birne Binegar: I would do right.
Birne Binegar: Here you see.
Birne Binegar: evening do perfectly good equal to X plus y plus equals might also have a perfect vacation but they're contradictory because it's too busy at work would be well I tried to do it, then this will look like hear people in here so happy.
Birne Binegar: So this parable only be true if the other two is the number minus one which is all.
Birne Binegar: And in fact we have this graphic is bought separately plotting each solution and then i'm 13.
Birne Binegar: Total fluke hydroplane never dealt with the situation that you have contradictory way JESSICA.
Birne Binegar: Alright, so it's um.
Birne Binegar: yeah so here's a general what happened, we have to explain.
Birne Binegar: What happened hey guys.
Birne Binegar: show this again visually.
Birne Binegar: If you have.
Birne Binegar: equation.
Birne Binegar: There are solutions that are going to be the intersection of the course on.
Birne Binegar: What will happen if the intersection of.
Birne Binegar: Why, I played.
Birne Binegar: one.
Birne Binegar: The other possibility.
Birne Binegar: You ever play like that will happen.
Birne Binegar: If you have.
Birne Binegar: If you play every day.
Birne Binegar: Oh that's.
Birne Binegar: pretty clear for.
Birne Binegar: Two equations and three variables.
Birne Binegar: Let me move on to the next case three linear equations three variables.
Birne Binegar: So let me use the word as representing solution set apart equation.
Birne Binegar: At this piece paper mache infinite represents a second now you see the intersection of the exactly where the paper beat the blackboard.
Birne Binegar: 30 equation straight, you would see that, on the common point the point that common for all three planes is actually going to be a simple form.
Birne Binegar: So what happens is.
Birne Binegar: Every time I asked equation solutions that.
Birne Binegar: Actually, what you can and that's the general you have three equations and three and number five number is getting.
Birne Binegar: solution.
Birne Binegar: Really by three zero.
Birne Binegar: not interpret zero it's a there's no solution.
Birne Binegar: it's saying that the solution is zero.
Birne Binegar: Point wait wait we can't even think of our degrees of freedom, the part that.
Birne Binegar: We have a dinner.
Birne Binegar: table point we just didn't go anywhere from a quarter.
Birne Binegar: Okay, OK, so now.
Birne Binegar: Social Here again, the first.
Birne Binegar: Three equation equal importance on hyper plane and what's.
Birne Binegar: likely to happen, the.
Birne Binegar: Second point both you Thank you have a unique solution system.
Birne Binegar: The whole reason I say that all equation.
Birne Binegar: But, of course.
Birne Binegar: More things can happen more number of variables speaking more number on the larger number of equations.
Birne Binegar: And so.
Birne Binegar: The real world problems course.
Birne Binegar: Gavin is like.
Birne Binegar: Your are you have three equations.
Birne Binegar: That doesn't always happen.
Birne Binegar: So here we have three equation.
Birne Binegar: And i'm not sure, either through like a story starship I have read three plain.
Birne Binegar: Black 41 and I have to other places that are intersecting and apparently there intersecting on the line, which is wanting.
Birne Binegar: How did that happen.
Birne Binegar: I don't see an audience on picture or a year yet somehow.
Birne Binegar: After posting three equations of variable i'm sitting and go point for solution, what happened, you, you have.
Birne Binegar: This stage is.
Birne Binegar: If you add the first equation equation is like that that.
Birne Binegar: track, you know, the second equation X minus zero here, why mining know why.
Birne Binegar: Why, and the.
Birne Binegar: Next.
Birne Binegar: slide yeah okay.
Birne Binegar: yeah that's right there we go yeah.
Birne Binegar: I have three.
Birne Binegar: Three points of intersection along the line we are getting therapy.
Birne Binegar: Because the third equation is already invited by the first.
Birne Binegar: Just these you.
Birne Binegar: know.
Birne Binegar: y plus y y T minus the invoices one plus one is.
Birne Binegar: Two equations to equate that automatic true.
Birne Binegar: Across linear algebra.
Birne Binegar: display this alarm not going to be a resident on the equation.
Birne Binegar: or matrix technique.
Birne Binegar: In addition, it's also going to expose contradiction.
Birne Binegar: working toward it out all the technical instruction or general whoo.
Birne Binegar: All right, yeah and then here's an example of.
Birne Binegar: visual thing what happens when you have free.
Birne Binegar: comprehension.
Birne Binegar: problem will be well worth it would be very fine there's no there's no sleep at all.
Birne Binegar: Okay, so that's the main point.
Birne Binegar: Of today's lecture.
Birne Binegar: Is.
Birne Binegar: wonderfully.
Birne Binegar: lyrically and unknown when you should expect to have 99.9% of the time and the boy is a solution that number variable.
Birne Binegar: Variable.
Birne Binegar: However, if there are some.
Birne Binegar: that's going to be, not all of the equation or effective.
Birne Binegar: It can be redundant data.
Birne Binegar: Where the price of the solution is going to be an equation that already implies.
Birne Binegar: Well matted hair your solution that might be bored and my evil.
Birne Binegar: or a big contradiction.
Birne Binegar: method be prepared to find the.
Birne Binegar: middle.
Birne Binegar: Okay, so that's.
Birne Binegar: good enough for today on.
Birne Binegar: Wednesday we'll do it.
Birne Binegar: again.
Birne Binegar: And i'll introduce the matrix technique to do.