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.  -5(A+D)

Accepted Answer

Welcome back. I am so glad you're here. We are given two matrices, P and Q. And we're to perform the mentioned matrix operation. Well, that mentioned matrix operation is right here, that is negative three times parentheses, P plus Q. So what do we do first here we're going to start with what's inside the parentheses. We're going to add P and Q together. So I'm going to copy down P and Q. So P is and I'm going to start just reading columns. So first column is 214, 2nd column is 102, 3rd column is negative 236. And we're adding that to Q. Starting with the first column of Q. That is 1 -3, 2 -1, is the second column and the third column is 415 adding those together. We are going to add similar position to similar position. So the first row, first column from each matrix matrix. So first row, first column from the first one from P is to first row. First column from Q is one, so two plus one is three. Now I'm just going to continue down the first column for each matrix. So the second row, first column from P is one plus, second row, first column of Q is negative 31 plus negative three is negative two. And finishing the column. The third row first column of p is four plus. The third row, first column of Q is two, so four plus two is six. I'm going to go a little bit faster, going down the second column of each one adding them together. One plus negative one is 00 plus three is 32 plus zero is too. Now the third column negative two plus four is a positive 23 plus one is four and six plus five is 11. So now we have performed the addition operation and now we need to multiply this whole thing times negative three. So we're going to take that negative three and distribute it to every position in the matrix. So starting with the first row, first column multiplying three times negative three is negative nine, proceeding down the column negative two times negative three is a positive 66 times negative three is negative 18. Starting in the second column, zero times negative three is 03 times negative three is negative nine and two times negative three is negative six. And now the final column two times negative three is negative 64 times negative three is negative 12 and 11 times negative three is negative 33. Alright. We have performed all of the operations. Now looking at our answer choices, this matches with answer choice a Well done. We'll catch you on the next one

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. -5(A+D)

Key Concepts

Matrix Addition

Scalar Multiplication

Matrix Dimensions

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