In Exercises 27 - 36, find (if possible) the following matrice...

Question

In Exercises 27 - 36, find (if possible) the following matrices: a. AB b. BA 1 - 1 4 1 1 0 A = 4 - 1 3 B = 1 2 4 2 0 - 2 1 - 1 3

Matrices A and B for matrix operations in college algebra, chapter on matrices and determinants.

Accepted Answer

find the given matrices if possible. For A is p Q b is QP. So we want p times Q first. Now we can all have multi matrices together if the number of rows and our first matrix has the same number of columns as our second matrix. You notice here we have three rows and P three columns. And cute so we can multiply those together. So that's where we're not the multiplication for us. But how we go about this as we look at our first ropey two negative 32 and multiply it by first column Q 417. And we multiply the First Index two and 4. First the two times for the first negative three times one, be next, so negative three times one. And finally two times seven. Which gives us to some seven there at the end. They'll give us the first term of our matrix. Our first index. Rather We'll have nine different places in our matrix because we have a three x three result. After multiplying. So I both fight it out for us. And we notice here our 1st 1 two times four plus 93 times one plus two times seven. We add all this together. You get eight -3 Plus 14. That gives us 19 four plus nine plus four. It's a 17 and zero plus three plus two gives us five. Next part four plus five plus 21 gives us two -15 Plus five. I'm sorry about that plus six gives us negative seven In 0 -5 plus 3 -2. Follow 1, 43. 0 -3, 12 gives us nine. And finally zero native one and six. And also the other that gives us five. My matrix p Q. Is that now? You do the same for? QP. Thank you. You have eight plus two plus zero. Which is 10 negative 12 plus 10 plus zero negative two and eight plus six plus 0 14. Next we have 2 -3 plus. You know, That gives this negative one. -3 -15 -1. That gives us - And 2 -9 -6. That gives us -13. Bottom. We have 14 plus two plus 0, 16 negative 21 plus plus one. That gives us -10. Finally 14 plus six plus six. That gives us 26. So we have both major cities now P. Q and Q. P. If you look over our answers, we can see our answer corresponds to answer B. This center matrices right here. Okay. I hope to help you solve the problem. Thank you for watching. Goodbye

In Exercises 27 - 36, find (if possible) the following matrices: a. AB b. BA 1 - 1 4 1 1 0 A = 4 - 1 3 B = 1 2 4 2 0 - 2 1 - 1 3

Key Concepts

Matrix Multiplication

Dimension Compatibility for Multiplication

Non-Commutativity of Matrix Multiplication

Watch next