Solve for X in the matrix equation 3X+A = B where

Question

Solve for X in the matrix equation 3X+A = B where <Image>

Accepted Answer

Welcome back. I'm so glad you're here. We have got two matrices, P and Q. And we're going to perform some operations with them in order to find X. So I'm going to copy this down here. Two X plus P equals two Q. And now I can scroll down a little bit and you can see all of the answer choices. So if this were just algebra, how would we sell for X? How would we get X by itself? Well, we'll subtract P from both sides. That will cancel out the PS on the left. So we've got two X equals two Q minus P. And now let's divide both sides by two to cancel out on the left. So now we've got X equals two Q minus P in the numerator divided by two in the denominator. So what are the operations that were going to be performing here? Let's take a look and see what we're going to do first. Well first we're going to take um we're going to look at the numerator because that's an invisible parentheses and we'll work on that. First, the first thing we'll do is multiply that Q by two. So step one will be two Q. And then after we've got two Q we will take two Q and subtract the value of P. And once we've got to Q minus P, We will divide everything by two groups. And once we've done those three steps we'll have X by itself will have solved for X. So let's work on that first step here to Q. Well, if Q equals copy this down 25, -1, then two Q. Will be multiplying everything in Q by two. So right times two times two times two times two. So our new matrix for two Q will be two times two is 45 times two is 10. 8 times two is 16 and negative one times two is negative two. Got step one done. Now Let's work on step 2 to Q -P. Well we have got our two Q. And we're going to subtract the corresponding values in R. P. Matrix. So for four the corresponding value is one. So we'll take four minus one for 10. The corresponding value is zero. So we'll take 10 minus zero. For 16. The corresponding value is zero. So we'll take 16 minus zero And for negative to the corresponding value is one. So we'll take -2 -1. So our new values for two q minus p will be four minus one is 3, 10 minus zero is 10, 16 minus 0, 16 and negative two minus one is negative three. We've got two steps done. Now let's do our previous 12 q minus P divided by two. And this will equal Well now let's look at two Q minus P and divide each one of these by two. Three divided by two will equal three halves, 10 divided by two is 5, 16 divided by two is eight and negative three divided by two is negative three halves. And that's it we've solved for X. We look at our answer choices and this matches with answer choice D. While done, we'll catch you on the next one.