In Exercises 14–27, perform the indicated matrix operations gi...

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. 3A+2D

Accepted Answer

Welcome back. I am so glad you're here. We are given two matrices, P and Q. Were asked to perform the mentioned matrix operation. The mentioned matrix operation is right here, it's two times p minus three times Q. So what do we do first? First we're going to do this multiplication. We're going to take two times P and then we'll take three times Q. And then finally we will subtract those from each other. So I'm going to start off by copying down P and Q. So I'm going to start reading the first column. I'm going to read it straight down. So for P it is 214, 2nd column is 102, 3rd column is negative 236, that is P. And then Q is starting with the first column, one, negative 32, 2nd column negative 130. 3rd column is 415. Okay. And P will work with P first P we're going to multiply everything times two that two gets distributed to every position in the matrix. So now this will read I'm going just down the columns again. So two times two is times two is 24 times two is eight. Second column one times two is two. Zero times two is 02 times two is four. And the third column negative two times two is negative 43 times two is six and six times two is 12. So there is R two p And now let's work on our three Q. We're going to multiply everything in Q times three and distributing that. I'm going to read column by column. So starting with the first column one times three is three negative three times three is negative nine and two times three is six. Second column negative one times three is negative 33 times three is nine and zero times three is zero. The third column four times three is 12, 1 times three is three and five times three is 15. All right now we have done the multiplication and the next step is to subtract these two matrices. So we are going to subtract similar position from similar positions. So for example, the first row, first column in p minus the first row, first column of Q. So first row, first column of P is four minus first row, first column of Q is 34 minus three is one. I'm going to continue down the columns. So first column, second row of p is two minus. The first column. Second row of Q is negative nine, so that's two minus negative nine which is two plus nine, so that is 11. And then we've got the first column, third row of pea which is eight minus the first column, third row of Q which is six, so eight minus six. That is to I'm going to do the second column a little bit faster. So this is two minus negative three which is two plus three which is five, 0 -9 is -9 and 4 0 is four. Now the third column negative four minus 12 is negative 16, 6 -3 is three And 12 -15 is -3. So we have performed all of those operations. Now we look at our answer choices and this matches with answer choice D. 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. 3A+2D

Key Concepts

Matrix Operations

Matrix Dimensions

Scalar Multiplication

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