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> BD

Accepted Answer

Welcome back. I'm so glad you're here. We've got two matrices and we're to perform the indicated operation here. And that is multiplication. We're multiplying p times Q. So I will write these a little bit bigger. We've got P equals first row of P is 21 negative one. 2nd row of P is 3-4 and Q has three rows. The first row is 10, 2nd row is 22, and the third row is one negative one. To multiply these. We are going to take the rows of P and multiply them by the columns of Q. I'll show you what that looks like. So we look at the first row of P, the first one, we're going to move from left to right. The first one is to we're going to multiply that by the first term in the first column of Q, which is one, so two times one. And then we're going to add that to the second term from the first row of P, which is one times the second term from the first column of Q. Which is to and then add that to the third term in the first row of P which is negative, one times the third term in the first column of Q, which is one. Then we put a little bit of space and we're going to work with the first row of pea again. But now we're going to take the first row of P and multiply it by the second column of Q. So the first term in the first row of pea is to again times the first term in the second column of Q which is zero plus the second term in the first row of P which is one times the second term in the second column of Q. Which is to plus the third term in the first row of P which is negative one times the third term in the second column of Q, which is negative one. And that's the first row. Now we look at the second row of pea, we're going to repeat the process. We're going to take the second row of P times the first column of Q. So the first term in the second row of P is three times the first term in the first column of Q. Is one plus the second term in the second row of Pea which is two times the second term in the first column of Q. Which is to plus the third term in the second row of P, which is four times the third term in the first column of Q, which is one. Then we leave a little bit of space. We're going to repeat P. S. Second row. So starting with the first term, that's three times cues second columns, first term which is zero plus the second term in the second row of pea which is two times the second term in the second column of Q which is two plus the third term in the second row of P which is four times the third term in the second column of Q. Which is negative one. And if you've done it correctly you should see these terms in the parentheses, lining up with each other. So that's a good clue. You've done it well probably. And now let's take these and do the multiplication that we've set up. So starting with the first row, two times one is two plus one. Times two is two plus negative one times one is negative one leave a little space, two times zero is zero plus one times two is two plus negative one times negative one is positive one. Now the second row three times one is three plus two times two is four plus four times one is four. Three times zero is zero plus two times two is four plus four times negative one is negative four. Now let's do that. Addition. Two plus two plus negative one is three. Zero plus two plus one is three. Three plus four plus four is 11 and zero plus four plus negative four is zero. That matches with answer choice B. Well done. We'll catch you on the next one.