In Exercises 9 - 16, find the following matrices: b. A - B
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Question

In Exercises 9 - 16, find the following matrices: b. A - B

Matrices A and B for exercise 15 in college algebra, chapter on matrices and determinants.

Accepted Answer

Hey everyone welcome back in this problem. We are asked to perform the following matrix operation and the operation is A minus B. They were given A and B as 23 by three matrices. Now let's go ahead and write what we want to find A minus B. And let's write this in terms of the matrices. So A in the first column is 375. And the second column is negative 22 negative one. And then the third column is negative 3 to 0. Okay? And that's gonna be minus B. And B. In the first column 10, negative two. In the second column to negative 61. And in the third column negative eight negative three and five. Alright, So the first thing we want to do and we're subtracting matrices is double check that they have the same dimension. So in this case we have 23 by three matrices case. We're okay to do the subtraction. And when we do the subtraction, we're going to do an element wise, what that means is we're gonna take an element in A. Okay, And we're going to subtract the corresponding element in matrix B. Okay. And put it into our new matrix. Now our new matrix is going to be the same size, same dimension as A and B. All right, so let's see this in practice. So we're gonna take the first row. First column of A. We get the element three. Okay, we're gonna do the corresponding element and be so first row. First column we have one. Okay, our operation is subtract. And so in the first column and first row of our new matrix we're gonna have three minus one. We can do the same thing for the next row. Okay? So second row, first column we have seven in matrix A. In the same position we have zero and matrix B. And so in the second row, first column of our resulting matrix we're going to have seven minus zero. Alright, we're gonna do the same thing for all of the other terms. So in the bottom left we're gonna get 5 -2. Okay. Second column, first row we're gonna get negative two minus two. Second column, second row we get two minus negative six and second column, third row we get negative one minus one. Moving on to the third column. The first row, third column we get negative three minus negative eight. The second row, third column we get two minus negative three. And the third row, third column we get zero minus five. All right now, it's just regular addition and subtraction. Ok. To simplify this matrix we have it down to one matrix we just need to simplify. So three minus one. We're going to get to seven minus zero is seven. We're gonna get seven in the third row. First column. Working in the down along the second column we get negative four, 8 -2 and in the third column we get five. Five negative five. Alright. And so this is the resulting matrix a -1 that we were looking for. And this is going to be the matrix two negative 45 in the first row, 785 in the second row, and seven negative two negative five in the third row. Okay. And that's going to correspond with Answer C. That's it for this video. I hope that helped. Thanks for watching.

In Exercises 9 - 16, find the following matrices: b. A - B

Key Concepts

Matrix Subtraction

Matrix Dimensions

Element-wise Operations

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