Let

Question

Let

A = [\begin{matrix} - 2 & 4 \\ 0 & 3 \end{matrix}]

and

B = \left[ \begin{matrix} -6 & 2 \ 4 & 0 \end{matrix} ight]

. Find each of the following.

-A + (1/2)B

Accepted Answer

Hello, everyone. We are asked to find the value for the following expression if matrix A is a two by two matrix with the first row as negative 59 and the second row as 0 11. And matrix B is also a two by two matrix with the first row as negative 12 6. And the second row as 90. The expression we are evaluating is negative A plus one third B. Our answer choices are all two by two matrices and in each one, a different element is negative. But we have four possible answer choices filling in the expression using the matrices. I'm gonna have negative A. So that's like negative one multiplied by the matrix negative 59 for the top row 11, for the second row plus one third multiplied by matrix B. So negative 12 6 is the top row +90 is the second row. Recall that when you're multiplying a matrix by a single value, we multiply each element in that matrix by that value. So each element in the first matrix will be multiplied by negative one. So we'll have negative one multiplied by negative five in the top left corner, negative one multiplied by nine in the top right corner, negative one multiplied by zero in the bottom left corner, negative one multiplied by 11 in the bottom right corner. I'm gonna do the same with the one third. I'm gonna multiply one third by negative 12 in the top left corner, one third multiplied by six in the top right corner, one third multiplied by nine in the bottom left corner and one third multiplied by zero in the bottom right corner doing out my multiplication. My first matrix is top row five, negative nine, bottom row zero, negative 11. We're gonna add that to the second matrix which when I multiply each element by one third, I get negative four is my top left corner two is the top right three is the bottom left zero is the bottom right. Now, recall when we add two matrices together that we add the corresponding elements. So we are going to add five plus negative four for the top left corner, which would be one negative nine plus two for the top right corner, which is negative 70 plus three for the bottom left corner which is three negative 11 plus zero, which is negative 11 in our bottom right corner. This means the answer here is a two by two matrix where the top row is one negative seven. The bottom row is three negative 11 and this matches answer choice D have a nice day.

Let $A = [\begin{matrix} - 2 & 4 \\ 0 & 3 \end{matrix}]$ and $B = \left[ \begin{matrix} -6 & 2 \\ 4 & 0 \end{matrix} \right]$ . Find each of the following.
-A + (1/2)B

Key Concepts

Matrix Addition and Scalar Multiplication

Negative of a Matrix

Matrix Dimensions and Compatibility

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