In Exercises 9 - 16, find the following matrices: d. - 3A + 2B...

Question

In Exercises 9 - 16, find the following matrices: d. - 3A + 2B

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

Accepted Answer

everyone in this problem? We are asked to perform the following matrix operation and the operation is five A minus three B. A and B are two by two matrices. A is given by first row seven to second row 68, and B is given by the first row 13 and the second row to six. Alright, so we're asked to do five A minus three B. Okay, so let's write this out in terms of our matrices. So we have five times A. Which is 76 in the first column to eight in the second column minus three B. Which is 1, 2 in the first column and 36 in the second column. Alright, so when we're doing multiplication and addition, subtraction, we're multiplying by a constant and we're adding and subtracting matrices, we want to do that multiplication first. Okay, Before we go and add and subtract. So let's do that first. So when we're multiplying a matrix by constant, we can bring that constant inside the matrix. And we're going to multiply element wise. So every single element of that matrix is going to get multiplied by that constant. Okay, so for five times A we're going to get the matrix With first column five times 7 and five times and second column five times two and five times eight. Okay, so we brought that five in and multiplied it to every element. Now we have subtraction. We're going to do the same for three B. Okay, we're gonna bring that three in and multiply it to each element. So we get three times one. Three times two. Three times three. Three times six. Alright, so we've done that. We've done our multiplication by constance. Let's just expand the product. Okay, so five times seven is gonna give us 35 5 times 6. 35 times 2, 10 and five times 8 40. We're gonna subtract three times 133 times 263 times 39 and three times 6, 18. Okay, So now we are just subtracting two matrices. How do we deal with subtraction? But we do it element wise. Okay, so we take an element in matrix. The first matrix and we're going to subtract the corresponding element from the second matrix. In this case the first matrix is five A. The second matrix is negative three B. All right, So let's see what this looks like. So, again we take an element from the first matrix. Okay, so take the top left. We have 35. We take the corresponding element from the second matrix in this case three. And our operation is subtract. So we subtract the two and we put it in the same location in the new matrix. Okay, so 35 -3. Okay, when you're doing subtraction here, notice that these are both two by two matrices, you need the matrices to be the same dimension. In order to do the subtraction. And the matrix that you get as a result is going to be the same dimension as well. Alright, so we've done the first row, first column. Let's now do the second row. First column. In the first matrix we have 30 In the second matrix we have six. And so we're gonna end up with 30 -6. Okay, let me just color these. So you can see where they came from. Alright, so doing the second column, same thing in the top right? We're going to have 10 -9 and in the bottom right, we're gonna have 40 -18. Alright, so this is going to give a result five a -3. B is equal to 35 -3. Is 32. 30 minus six is 24. 10 minus nine is one and 40 minus 18 is 22. Okay, and so this is the resulting matrix it is a two by two matrix. First column 32 24. And second column 1 22. Okay. And just looking at the possible answers here, we scroll down. We see that this is going to correspond with answer. D. Thanks everyone for watching. I hope this video helped see you in the next one.

In Exercises 9 - 16, find the following matrices: d. - 3A + 2B

Key Concepts

Matrix Addition and Scalar Multiplication

Matrix Dimensions and Compatibility

Order of Operations in Matrix Expressions

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