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. 2X + A = B

Accepted Answer

Hey everyone in this problem? We are asked to solve the following matrix equation for X. Okay. The equation we're given is four X minus A. Is equal to B. And were given matrices A and B. Okay, so we have four x minus A. Is equal to be the first thing we wanna do. We want to solve for X. So let's go ahead and isolate X. Now, before we plug in our matrices. Ok. It's easier to do it now rather than moving and rearranging with matrices. So this is going to give us four. X. Is equal to B plus A. Okay. And we get X is equal to 1/4 times B plus A. Substituting in our matrix matrices. Sorry, we're gonna get 1/4 times B plus A. Which is gonna be let me make this around brackets. It's not confusing that that's a matrix OK. B negative 975 in the first column. Negative 200 in the second column. Okay. Plus A. Which is negative 610 in the first column. Negative four. Negative 83 in the second column. Okay. Alright. And so we have these brackets around B plus A. So we want to go ahead and do that addition. First. Before we multiply the constant out front. Okay. When we're doing matrix addition, we want to double check that the dimension of the matrices is the same. In this case we have three by two. Matrix for both of them. So the dimension is the same. We can do the addition. Okay. When we add matrices we're gonna add element wise. And so what that means is we're going to take an element in the first matrix We're going to add it to the corresponding element in the second matrix. Ok. So what we're going to see? So we have 1/4 times and we're gonna get the matrix and again take an element from the first matrix. Okay. So we're gonna take the first row. In the first column we get -9. We're going to do the same from the second. Matrix. Row one column one we get negative six. Okay. And our operation is add So we're going to add them together in the same position. In the resulting matrix. Okay, so in row one column 1. Okay, we can do the same thing with the next element. So row two column one. We have a seven and the first matrix we have a one in the second matrix. Okay, So in row two column one of our resulting matrix we're gonna have seven plus one. Okay? And we can do the same for all of the other terms. So in the final row of the first column we have five plus zero. And then in the second column we're going to get negative two plus negative four zero plus negative 80 plus three. Alright, so simplifying the matrix that we've just found before we do the multiplication. So we have 1/4. And again this is x one of our four negative nine plus negative six. That's going to be negative 15. Seven plus one gives us 85 plus zero gives us five negative two plus negative four. That's gonna be negative six. Zero plus negative eight is going to be negative eight and zero plus three is three. Alright, so now we are down to just this one. Matrix with a constant multiplied up front. Okay? When we have a constant multiplied up front, what we do is we can bring it into the matrix and multiply it by every single element. Okay. So what we're gonna get is we're gonna get negative divided by four, eight divided by four, five divided by four. Okay. And in the second column negative 6/4 negative 8/4 and 3/4. Alright, so let's give ourselves A bit more room here and this is going to give us an X. That is equal to okay, just simplifying within here we get negative 15/4. Let's give ourselves more room. Okay. 8/4 is two. And then we have 5/4. And in the second column negative 6/4. Well that's going to be negative three halves negative 8/4 is gonna be negative two and 3/4. And so this is the X. Value that we get when we solve that equation or? Okay and we get negative 15/4. 2 and 5/4 in the first column and negative three half negative two and 3/4 in the second column. Okay. And that is going to correspond with the answer a here. Okay. Thanks everyone for watching. 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. 2X + A = B

Key Concepts

Matrix Addition and Subtraction

Scalar Multiplication of Matrices

Solving Matrix Equations

Watch next