Find each sum or difference, if possible. See Examples 2 and 3.

Question

Find each sum or difference, if possible. See Examples 2 and 3. <1x4 Matrix> - <1x4 Matrix>

Accepted Answer

Hello, everyone. We are asked to calculate the difference for the given matrices. If possible, we have 24 by one matrices. The first one has a column that reads five A plus B two P plus four Q seven R minus three S negative two X plus Y. Our second matrix, the column reads two B minus six A nine P plus three Q R minus two S two X minus Y, we have four answer choices three of which are four by one matrices. And one says the difference does not exist. Recall that when we subtract matrices, they must be the same dimensions. In order to be subtracted. As I mentioned, we have a four by one matrix and we're subtracting another four by one matrix from it. This means we can do with this subtraction. And so we are going to subtract corresponding elements. And our answer will also be a four by one matrix. So in the first element of the column, we have five A plus B and we're gonna subtract the first element of the second matrix. So two B minus six A and I put two B minus six A in parentheses. Because we are subtracting the entirety of that expression. Next, we have two P plus four, Q is our second element in that column. We're gonna subtract in parentheses. Nine P plus three Q closed parentheses. Next element down seven R minus three S and we're subtracting in parentheses, R minus two S and the fourth element negative two X plus Y minus in parentheses, two X minus Y close parentheses. So now I'm going to distribute the negatives into the parentheses that follow them. And then we'll combine our like terms. So our first element, we have five A plus B minus two, B plus six. A second element two P plus four, Q minus nine, P minus three, Q third element seven R minus three, S minus R plus two S and the fourth element negative two X plus Y minus two X plus Y. So now that we have all of the signs, we are going to combine our lake terms. So for the first element starting with the A's, I end up with 11 A minus B second element, I'm gonna do P S before QS. So negative seven P plus one, Q or just Q third element. When do R before S so I have six R minus one S or just S and then the last elements of the fourth one down, I'm gonna do the XS first. So I have negative four X plus two Y. So our solution matrix is a four by one matrix and reading down the column, we have 11 A minus B negative seven P plus Q six R minus S and negative four X plus two. Oops, I'm sorry. That's two. Y, let me add that Y back in there for you. And when we check our answer choices, this appears to match answer choice. C have a nice day.

Find each sum or difference, if possible. See Examples 2 and 3. <1x4 Matrix> - <1x4 Matrix>

Key Concepts

Matrix Addition and Subtraction

Matrix Dimensions

Element-wise Operations

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