In Exercises 14–27, perform the indicated matrix operations given...

Question

In Exercises 14–27, perform the indicated matrix operations given that and D are defined as follows. If an operation is not defined, state the reason. <Image> -5(A+D)

Accepted Answer

Welcome back. I'm so glad you're here. We've got two matrices, we've got matrix P and matrix Q. So not A and B. P and Q. And we're going to perform the indicated operation which is listed here negative three times parentheses P plus Q. So let's get started by adding P plus Q. P plus Q. For matrices we're just going to add the corresponding position. So this upper left hand one gets added to this upper left hand one and so on. So starting off with two plus one is going to give us three and we're going to work across the row. So next one plus negative one is going to be zero. We'll finish the row negative two plus four is going to be too continuing on the second row and we'll work from left to right. We've got one plus negative three is going to be negative two and continuing zero plus three is going to be three and three plus one is going to be four. Now we'll finish up with the third row. Four plus two is six, continuing two plus zero is two and six plus five is 11. So we've added P plus Q. Now we're going to multiply it by negative three. So we're going to take everything here, times negative three, negative three gets distributed to every number in there. So again, starting with the upper left, we've got negative three times three is going to be negative nine will continue across the row, negative three times zero is zero negative three times two is negative. Six. Starting with the next row here negative three times negative two is positive, six negative three times three is nine negative nine negative three times four is negative 12. Now the third row negative three times six is negative 18, negative three times two is negative six, and negative three times 11 is negative 33. We look at our answer choices and this is going to match answer choice. A well done. We'll catch on the next one.