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 3 3 - 2 A = B = 5 3 - 1 6

Matrices A and B for exercise 27 in college algebra, chapter on matrices and determinants.

Accepted Answer

Find the given matrices if possible or have matrix PQ and QP. Now we're gonna multiply these matrices together. We can only multiply if the number of rows and our first matrix is equal to the number of columns in our second matrix. We now see that both of these are two by two matrices. So we will be able to multiply them together. This will result in a two by two matrix. Let's do PQ first. Now we multiply matrices gonna take the first row from P 31 and multiply it by the first column of Q negative five and zero. So we have three times negative five because those are our first terms in our emergencies. And then we add the 2nd 1 to 0. Now I do the same with our first row and our second column of Q three times eight of one plus one times two bottom left. We will take our second row multiplied by our first column negative two. I'm saying the fifth plus five times zero. And finally, you will take negative two times negative one plus five times two. You can simplify this, you will get negative 15 plus zero. Negative 15, negative three plus two, negative one negative 10, I'm sorry, positive 10 plus zero plus 10 and two plus 10 is 12. This is for our matrix PQ. Now let's look at QP, we did the same thing but with our rows of Q columns of P. So our first row negative the 5th, 1st part of the first column plus negative one multiplied by negative two, next part negative five by one plus negative one times five and then 95 85. Now we are in the second. So you actually want this to zero, zero times three plus two times negative two and zero times one plus two times fat. And we can simplify, we should get up negative 15 plus two, negative 13, negative five minus five, negative 10, zero minus four, negative 40 plus 10. What the thing that gives us 10, if you look at that, we should get negative 13, negative 10, negative four and positive tip. So PQ native 15 native 1 10 and 12 that corresponds with answer D as is QP negative 13, negative 10, negative four and 10, which means the answer to our problem as answer D OK. I hope to help you solve the problem. Thanks for watching. Goodbye.

In Exercises 27 - 36, find (if possible) the following matrices: a. AB b. BA 1 3 3 - 2 A = B = 5 3 - 1 6

Key Concepts

Matrix Multiplication

Matrix Dimensions and Compatibility

Non-Commutativity of Matrix Multiplication

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