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Question

Rewrite the (numerical) matrix equation below in symbolic form as a vector equation, using symbols $\mathbf{v}_{1}, \mathbf{v}_{2}, \ldots$ for the vectors and $c_{1}, c_{2}, \ldots$ for scalars. Define what each symbol represents, using the data given in the matrix equation.
$$
\left[\begin{array}{rrrrr}{-3} & {5} & {-4} & {9} & {7} \ {5} & {8} & {1} & {-2} & {-4}\end{array}ight]\left[\begin{array}{r}{-3} \ {2} \ {4} \ {-1} \ {2}\end{array}ight]=\left[\begin{array}{r}{8} \ {-1}\end{array}ight]
$$

Runpeng Li · Accepted Answer

All right. So for a problem, 28 we just need to apply. Apply our definition for the, uh, definitely 48 times, eight times acts. So, um, here we first need to notice that this is Ah. First were, uh the first matrix is to buy five. So that means we will have five vectors. That is all the columns. That is the So those five directors are from the columns of the giver and make 68 So just write down what you want me to be three and before and be fine. Okay. And since there are five actors, so there will also be five skaters. See? One seat too. C three, c four and C five. Okay, so here, See one. I just tried. I just tried to write down what these symbols mean. See, one or C, I will be the ice entry. Uh, vector. I&#x27;ll just write it down next of 3 to 4 to 12 Negative. Three to excuse me. Make it 32 or a negative one, too. Okay. And be won, or B, I missed three. I&#x27;ve column of the Given matrix, which is negative. 3592497 netting three by elected 497 and the second row is 581 elected to eight one active. Too active. So that&#x27;s it for it&#x27;s for our solution for quiet problem 28.

Bobby Barnes · Answer

So if they want us to rewrite this equation here, um, to the vector sum, what will do is what We just take this negative too. So we multiply it by this first road here, so it&#x27;s going to be negative, too. And then we have 7 to 9 minus three, and then we take this negative five and then multiply this one by the second row. So this is gonna be negative. Five. And then you have negative 31 negative 62 And in the right side of the equation, will we just keep that as the same? So one negative line 12 negative four. And then we can just double check really quickly that these do actually equal each other. So if we were to do negative too. So this this isn&#x27;t really needed for this next step. So technically, we&#x27;re done at this point, But just to kind of make sure that these are equal. So over here we would distribute the negative tube, so that gives us negative 14 negative for negative 18 and six. And then we&#x27;re gonna add this to when we distribute the negative five. So that gives us 15 negative five negative. 30 of not negative. 30. Positive 30 and then negative. 10. And so is this equal to what we have over here? So let me just put, like, a little question mark. So let&#x27;s see. Negative. 14 plus 15 is one, so that&#x27;s good. Negative for plus negative. Five is negative. Nine. That&#x27;s good. Negative. 18 plus 30 is 12. That&#x27;s also good. Six minus 10. Negative for So yeah, it does look like that is good beer. So, again, this is just more kind of double checking. Um, that this answer is correct. And all we really needed to stop at was what we had in that red box there.

Nez Nikoo · Answer

Okay. The problem is giving us a one and a two. They want us right matrix. And after you write the Matrix, find the column vectors. So a one is minus two 04 Why this one? Minus one on a two years from the problem. Nine minus four, minus four zero and eight. So, as you see, this is a two by five. That means we could have five called vectors. And each victor basically is just this column 1st 1 second. 1/3 1 4th 1/5 1 So I rewrite it. Harnessed for nine is one zero minus four is one four minus four is out of column vector minus 10 and minus 18 That&#x27;s a lot of column vectors. That&#x27;s five of All right, guys. Thank you. Bye.

Michael Jacobsen · Answer

in this video, we have a matrix here multiplying a vector, giving us all together a matrix equation. One thing in linear algebra that&#x27;s very important, however, is to be able to walk from a matrix equation like this and write it also as a vector equation. So in order to get this into the form of a vector equation, we first start laying down the columns that come from the Matrix A the first Columnist five negative too. And we&#x27;re going to be scaling it. We scale by the entries that we see in the vector here. So place of five, then minus one will multiply the second vector of our matrix. One negative seven. The next scaler is three. So go plus three Multiply Column three of our matrix, which is negative 83 and then the last scaler from the vector is negative. Two. It multiplies the final column of our matrix, which is four negative five and recall. We have to make a equation. So don&#x27;t forget to copy negative eight and 16 then our work is complete. Since all we really want to do here is show the format of the vector equation. But you can also check a work if you like, by multiplying these results together and seeing if you get too negative. 8 16

Thomas Emment · Answer

Okay. We have Ah, normative matrix. Here on we&#x27;d like to write out as systems of linear equations each wrote will be a different equation on We see with this, Linus, the names on the right are what are is Our equations are equal to the constant on left. Here we have the coefficients in front of all of our variables. We&#x27;ll be taking the first column as our coefficient for X variable. Second column For why? On a third column for Zet. So taking our first rate, which is our first equation. We can see we have to access. We&#x27;ve got zero wise on one Zet we consume. This is equal to nine. Moving on to our second right, which is our second equation. We&#x27;ve got zero exits. We&#x27;ve got minus a Y on minus. Is that an obvious minus on? This is equal to five. And then for our third and final row, you could see you&#x27;ve got three exes. We&#x27;ve got single. Why? We&#x27;ve gotten those ads on this is equal to eight. On these are is our system off linear equations

Carson Merrill · Answer

So first we want to write this system as a vector equation. So with the vector equation, what this is going to look like is we write as individual vectors 85 and one, and those are all our X one components. And then we add that with all of our X two components, which is negative one four negative three x two and that&#x27;s going to end up equaling 412 So that&#x27;s how it looks like as a vector equation. And then we want to move it into a matrix equation. So if that&#x27;s gonna look like is a single matrix that combines these vector columns, so it&#x27;s gonna be 851 negative 14 negative three Time&#x27;s D vector x one x two, which equals R B vector for 12 and this is all coming from our eight x one minus x two equals four five x one plus four x two equals one and x one minus three x two equals two So we group all these X ones together, giving us 85 and one, and then the group all of our X two&#x27;s together giving us negative 14 and negative three and then the group All these to give together giving us 41 and two

Problem

Construct a $3 \times 3$ matrix, not in echelon f…

Problem 28 Medium Difficulty

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David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications

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David C. Lay, Steven R. Lay, Judi J. McDonaldLinear Algebra and Its Applications

Anna Marie V.

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David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications