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

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

Matrices A and B for exercise 11 in college algebra, chapter on matrices and determinants.

Accepted Answer

Hey everyone in this problem? We are asked to perform the following matrix operation. Were asked to do A plus B. Okay. And were given the matrices A and B. They're three by two matrices A has the first column +764. And a second column +158. And B has first column 418 and second column negative seven negative nine and zero. Okay. Now, when we're adding matrices, we want to double check that they have the same dimension. Okay, in this case A and B are both three by two matrices. So they have the same dimension. So we're okay to do the addition. Okay, so we're asked to find A plus B. Okay, and let's just write this out in terms of our matrices. So we have +764 in the first column + in the second column. Okay, plus 418 in the first column negative seven negative 90 in the second column of B. Now we're doing addition of matrices. Were doing the addition element wise. Okay. And what that means is we're going to take an element in A and add the corresponding element and matrix B. Okay. Alright, so what this looks like. So let's start with the first element in matrix A. Ok, so the first row of the first column, we have a seven. Okay, we're gonna look at the exact same position in matrix B. So first row, first column and we have a four. Okay, and so this first row first column of our resulting matrix is going to be seven plus four. Okay, we add the two together and we put it in the same position. Okay, moving on to the next row. Okay, so row two column one. We have a six and A. We have a one B. Okay, so this resulting matrix is going to have six plus one in that same position. Let's do the same for the others. So in the bottom left we have four and A and A and B. So we're going to get four plus eight in the same position of our resulting matrix Ok. In the top right, we have one in A. Okay, we're going to add the corresponding element from B Which is negative seven. Ok. And it's going to stay in the same position. In our matrix we have five plus negative nine in row two column two. And in the bottom. Right we get eight plus zero. Alright, so now we have one matrix. All we have to do is go ahead and add all of these terms within the matrix that we found. Okay, so we get seven plus four is 11. 6 plus one is 74 plus eight is 12. 1 plus negative seven is negative 65 plus negative. Nine is negative four and eight plus zero is eight. And so the result of A plus B is gonna be the matrix here. Okay. Where the first column is 11. 7. 12 And the second column is negative six negative +48. Okay. And that's going to correspond with answer A that's it for this video. I hope that helped see you in the next one.

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

Key Concepts

Matrix Addition

Matrix Dimensions

Element-wise Operations

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