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> 3A+2D

Accepted Answer

Welcome back. I'm so glad you're here. We've got these two matrices, P and Q. So not A and B. That's okay. We've got P. And Q. And we're going to perform the indicated operations here. So we're going to have to p minus three Q. And in order to do that, we're going to start by multiplying two times P. And we're going to multiply three times Q. So let's start with two times P. Two P will equal just distributing A to to every single number in that matrix. So starting in the upper left two times two is four and we're going to work our way across the road two times one is two and two times negative two is negative four. We finished the first row. We're going to start with the second row two times one is 22 times zero is 02 times three is six. And now for the third row two times four is 82 times two is four, and two times six is 12. Great. Got that one done. Now let's take a look at our queue. We're going to multiply Q times everything in Q times three. So our matrix three, Q. We're going to start by multiplying three by this one up here. So three times one is three. And working across the row, three times negative one is negative three. And finishing the road three times four is 12. Moving down to the second row three times negative three is negative nine continuing to the right three times three is 93 times one is three. Now finishing up the third row here three times two is 63 times 00 and three times five is 15. We have got both of those distributed and now we're going to do this process here in the middle of the subtraction, we're going to take everything in to p minus everything in three Q. And we're going to do that by matching our corresponding positions. So this upper left hand one, we're going to take that and subtract the upper left hand one of three. Q. So four minus three is negative one. No, it's one. Excuse me, four minus three is one. Now looking, we're working across the first row from left right, so two minus negative three is going to be a positive five And finishing out the row negative four minus is negative 16. Now we'll start with the second row, two minus negative nine is continuing zero minus nine is negative nine and six minus three is three. Now, we'll start with this third row, eight minus six is 24 minus zero is four, and 12 minus 15 is negative three. We look at our answer choices and that is going to match answer choice. D Well done. We'll catch on the next one