Perform the indicated matrix operations given that A, B and C ...

Question

Perform the indicated matrix operations given that A, B and C are defined as follows. If an operation is not defined, state the reason.

$A = [\begin{matrix} 4 & 0 \\ - 3 & 5 \\ 0 & 1 \end{matrix}], B = [\begin{matrix} 5 & 1 \\ - 2 & - 2 \end{matrix}], C = [\begin{matrix} 1 & - 1 \\ - 1 & 1 \end{matrix}]$

BC + CB

Accepted Answer

consider the following matrices. And perform the indicated operation where we have two matrices, A and B. And the operation we want is a B minus B. A. Let's look at a B 1st. So he had a P that is matrix A times matrix B. To solve this be one of multiple agencies. We can only multiply if the number of rows in the first matrix equals the number of columns. And the second matrix we notice here, matrix A. We have two roads, this one, this one and our second matrix we have two columns. This one and this one. So we can multiply those together those five. Hcs multiplying 22 by twos together. So we're gonna get a two by two matrix out of the result. In our top left index We're gonna take the three In our first row multiplied by the four in our first column. Gonna racist. I'll put it out a little bit further And we're going to add now the five which is the second part of our first row, multiplied by the -8. Which is the second part of our first column. Now that is our first index. Now look at the second index. The one on the top right means you want to take our first row multiplied by our second column. So we have three times negative two Plus five times 7. Our bottom left is going to be our second row are negative multiplied by our first column are 48. So we have negative one times four Plus six times -8. Finally our bottom right, it will be our second road time for a second column. So you have negative one times negative two Plus six times 7. Now you can simplify you will get 12 minus 40. Native six plus 35. Made of 4 - And two plus 42. Much simplified. And further we get negative 28, -52 and 44. That is our A. B. No I wouldn't find what B. A. Is. So we have P. A. Do the same thing. We will have our B. Which is our first row for native to In our first column of a 3 -1. So we have four times three. 1st plus -2 times negative one. Top red. We have four times plus negative two. What's five x 6. Bottom left we go to our second row negative eight times Plus seven times 1. I'm sorry but that that is a negative 1 -1. And then on the bottom right you'll have negative eight times Plus seven times 6 simplifying 12 plus two 20 minus 12. Now 24 minus seven And negative 40 plus which that simplifies once more To the Matrix 14 8 - and two. Finally we can do A B minus B. A. Now we know ap was our negative 28 negative 50 to 44. Subtract 14 8 - 31 2. No A B minus B. A. That is going to be -28 -14. 29 -8, -52 - and 44 -2, simplified even further. 28 minus 14 is negative 42. Joining the minus eight is 21 negative 52 minus negative 31. His negative 21 And finally 44 minutes to is 42. We can't simplify any further. So this is our matrix. And if we go back to our answers, we notice that the answer to our problem. It's answer. A Okay. I hope to help you solve the problem. Thanks for watching. Goodbye.

Key Concepts

Matrix Multiplication

Matrix Addition

Determining if an Operation is Defined

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