Let

Question

Let

A = [\begin{matrix} - 3 & - 7 \\ 2 & - 9 \\ 5 & 0 \end{matrix}]

and

B = [\begin{matrix} - 5 & - 1 \\ 0 & 0 \\ 3 & - 4 \end{matrix}]

Solve each matrix equation for X. X - A = B

Accepted Answer

Hey, everyone in this problem, we're given two matrices and we're asked to solve the matrix equation for X. OK. And the matrix equation we're given is X plus A is equal to B. We're given the matrix A as a three by two matrix with first column negative 610 and second column negative four negative 83. And B is a three by two matrix with first column negative 975 and negative 200. OK. So let's get started. We have our matrix equation X plus A is equal to B OK. We want to solve for X. So let's go ahead and do that now. OK. It's simpler to do it now before we have our matrices than to rearrange with the matrices afterwards. OK. So if we want to solve for X, we're gonna get X is equal to B minus A. OK. So in order to find X, we just need to subtract our two matrices. Let's go ahead and plug in our matrices. OK. So the matrix B first column negative seven or sorry, negative 975 and second column negative 200 minus the matrix A first column negative 610, negative four negative 83. OK. Now we're subtracting matrices. We wanna look and make sure that they are the same dimension. OK. We cannot subtract matrices that are different dimensions. So here we have 23 by two matrices. So they have the same dimension, they're the same size. So we can subtract OK. When we do subtraction with matrices, it's an element wise operation. So we're gonna take an element from the first matrix and subtract the corresponding element from the second matrix case. So we're gonna go term by term. All right. So what does that look like? Well, let's start with the first element. OK. So we're gonna take the first row in the first column, the first matrix we have negative nine and then the second matrix we have negative six. OK? So we're gonna subtract the two and we're gonna put them in the same position in a resulting matrix. So in row one column one, we're gonna have negative nine minus negative six. OK? And that comes from here. All right. Now we're gonna keep going down that column. So in the second row, first column, we have a seven in the first matrix and a one in the second matrix. OK. So we're gonna go ahead and subtract them and put them in the same position. So in row two column, one of our resulting matrix we have seven minus one. Yeah, we're gonna do the same for the rest of the matrix. So we're gonna get five minus zero in row three column one and then moving to the second column, we're gonna have negative two minus negative 40 minus negative eight and zero minus three. Hm This is gonna give us the resulting X matrix of negative nine minus negative six. That's going to be negative 37 minus 165 minus zero is 52 minus negative four or sorry. Negative two minus negative four is gonna be 20 minus negative eight is gonna give us eight and zero minus three is gonna give us negative three. OK? And so this is a matrix X that we were looking for. It's a three by two matrix with first column negative 365 and second column 28 negative three. And that's gonna correspond with answer C here. That's it for this one. I hope this video helped see you in the next one.

Let $A = [\begin{matrix} - 3 & - 7 \\ 2 & - 9 \\ 5 & 0 \end{matrix}]$ and $B = [\begin{matrix} - 5 & - 1 \\ 0 & 0 \\ 3 & - 4 \end{matrix}]$ Solve each matrix equation for X. X - A = B

Key Concepts

Matrix Addition and Subtraction

Solving Matrix Equations

Matrix Dimensions and Compatibility

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