In Exercises 9 - 16, find the following matrices: b. A - B4 1 5 9...

Question

In Exercises 9 - 16, find the following matrices: b. A - B4 1 5 9A = B = 3 2 0 7

Matrices A and B for exercise 9 in college algebra, chapter 7 on systems of equations.

Accepted Answer

Hey everyone, Welcome back in this problem. We are asked to perform the following matrix operation and that is a minus B. Okay. The matrices were given A and B are both two by two matrices. Ok. A has first row 72 and second row 68. And B has first row 13 and second row to six. Okay, Alright, so we want to calculate a minus B. So let's write this out in terms of our matrices. So we get 76 in the first column to eight in the second column minus B. 12 in the first column. 36 in the second column. Alright, when we're doing subtraction of two matrices, we want to double check that they have the same dimension. Okay. That's a requirement to do the subtraction in this case, they're both two by two matrices. So we can go ahead and do the subtraction. Now when we're doing subtraction, this is an element wise operations. Okay. And what that means is we're going to subtract the element from A with the corresponding element from B. Okay, we're gonna go element by element. Alright, so let's see how this works. So we're gonna take the first row, first column. It's gonna be a seven for a And we're going to subtract the first row, first column of B. Okay, so this is gonna be 7 -1 and we're going to put it in the same position of the resulting matrix. We're gonna do the same for the second row. First column. So in a we have a six. Okay. And we're going to subtract the same corresponding element from B which is a. Two. We're gonna put it in the same position in the matrix 6 -2 here on the bottom left. And we can do the same for the second column as well. So we're going to get to minus three In the top right? We're gonna 8 -6 in the bottom. Right now. We just need to do this regular subtraction for each of these elements and we'll have a result. So seven minus one is 66 minus two is 42 minus three is negative one and eight minus six is two. So we get the resulting matrix of a minus B. Is this two by two? Matrix with first rose six negative one and second row 42. Okay. That's going to correspond with answer C. That's it for this one. I hope this video helped see you in the next one.

In Exercises 9 - 16, find the following matrices: b. A - B4 1 5 9A = B = 3 2 0 7

Key Concepts

Matrix Subtraction

Matrix Dimensions

Element-wise Operations

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