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 15 in college algebra, chapter on matrices and determinants.

Accepted Answer

hey everyone in this problem we are asked to perform the following matrix operation and we have A plus B. And A and B are given as +23 by three matrices. Ok, So let's write out what we want to find. We want A plus B. Okay. And in terms of matrices we have A with the first column +375. 2nd column negative +22 negative one. And third column negative 3 to plus B. First column +10 negative two. Second column two negative +61. And third column negative eight negative three and five. Now, first thing when we're adding matrices, we just want to double check that they have the same dimension in this case. They're both three bed three matrices A and B. And so we're okay to do the addition. Okay. But the dimension does need to be the same. Now when we're doing addition of matrices we add element wise. What that means is we take an element in A. Okay. And we're going to add it to the corresponding element in matrix B. So let's see how this works. Okay, so we take the first row. First column K. The element here in matrix A is three. We look at the corresponding element in B. First row. First column, that's one and our operation is ad So we add them together three plus one. Okay? We put it in the same position in our resulting matrix. So it's going to be in the first row. First column. Now we can do the same. Moving down that column. So in the second row, the first column we have a. Seven and a second row. First column we have zero and B. And so this element is gonna be seven plus zero in our resulting matrix and we can do the same for the rest of the elements. Okay so the bottom left we're gonna have five plus negative two. In the second column. The first row we have negative two plus two, second row, second column two plus negative six. And second column third row negative one plus one. Moving on to the last column. In the first row we have negative three plus negative eight two plus negative three in the third column, second row and third column third row we have zero plus five. Now we have one matrix and we're just gonna simplify in that matrix to get our result. Okay so three plus 147 plus zero is 75 plus negative two is three. Okay, moving to the second column we're gonna get zero negative 40. And in the third column negative 11 negative one and five. Okay. And so this is our resulting matrix A plus B. That we were looking for K +23 by three matrix first row +40 negative 11. 2nd row seven negative four negative one and third row +305. And that's going to correspond with answer a Thanks everyone for watching. I hope this video 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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