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

Question

In Exercises 27 - 36, find (if possible) the following matrices: a. ABb. BA4 2 2 3 4A = 6 1 B = 3 5 - 1 - 2 0

Matrices A and B for exercises in college algebra, chapter on systems of equations.

Accepted Answer

find the given matrices if possible. Our first one says you want P. Q. So P huge. Is the matrix P times Q. Now we can only multiply matrices if in our first matrix the number of rows equal to the number of columns. In the second matrix we notice here P has three rows que has three columns so we will be able to multiply these. So let's take a peek you I want to multiply our first row by our first column, Anthony first, show by a second, calm. First by third, calm and so on. So we're actually gonna get a three x three matrix out of this because we have three rows and three columns. Our first one will be five, Then the first index of our com later three plus the 2nd +18 by the second part of our column zero. Now we'll do it again. Five. Our next column starts with two Plus eight times negative. five Hand five times plus eight times two. And then we keep going. Now we go to our next row negative one, 83 Plus three times 0. Then -1 times two Plus 3-5 and negative one times one plus three times two. Our last one, You start with the 9. 9 times out of three Plus two times 0, nine times two Plus two time state of five. Nine times one Plus two times 2. Now we can simplify our matrix five times negative. Three negative 15 plus zero. That is negative 15. We have five, some suit 10 -40, negative 30 five plus 16, three plus zero plus three negative one minus negative two -15 -17. Native one times one. Native one minus or plus six. Five, 1983. They had 27, 18 -10 gives us eight And nine plus 4 is 13. That this result for our matrix P. Q. Now let's find QP. Now similarly we have two rows and Q. Two columns and P. This time we'll actually get a two x 2 Matrix L. So the first one our first row negative three multiplied by our first column. P. So our first one is five Plus two times 8 of one Plus one times 9 and so on. That is our 1st 1. Top right, negative three times eight plus two times three plus one times two bottom left. You start with the second row, zero times five plus Native five times nine. I'm sorry. I need to find some snake one backwards and two times 9 and finally zero times of kate plus 95 times three Plus two times 2. You can simplify this. People get -15 -2 Plus nine. May of 24 plus six plus two, zero plus five plus 18 and 0 -15 plus four which results and negative 15 plus minus two, negative 17 plus nine negative eight. 24 plus eight negative 18 plus 5, 23 1915 plus four negative 11. Both matrices are simplified. If we notice the only answer that fits here. There's the answer. C. 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. ABb. BA4 2 2 3 4A = 6 1 B = 3 5 - 1 - 2 0

Key Concepts

Matrix Multiplication

Dimensions of Matrices

Order of Multiplication

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