Let

Question

Let Matrix A displayed as a 2x2 matrix with elements: -2, 4 in the first row; 0, 3 in the second row. and . Find each of the following. See Examples 2 –4.

2A + 4B

Accepted Answer

Hello, everyone. We are asked to find the value of the following expression. If A is a two by two matrix where the first row is negative 59 and the second row is 0 11 and B equals A two by two matrix where the first row is negative 6. And the second row is 90. We want to find the value of negative three A plus five B. Our answer choices are all two by two matrices A has first row 45 3. 2nd row, 45 negative 33 B. The first row is negative 45 3. The second row is 45 negative C. The first row is negative 45 3. The second row is 45 33 D. The first row is 45 3. The second row is 45 33. The first thing I'm gonna do is rewrite this so I can put my matrix in for my value. So I'll have negative three multiplied by the matrix where the top row is negative 59, second row is 0 11 and that is plus five multiplied by the matrix negative 12 6 for the first row +90. For the second row recall that when you multiply a matrix by a factor on the outside, we're going to multiply each element by that value. So I'm gonna multiply each element in the first matrix by negative three, negative three, multiplied by negative five is 15, negative three, multiplied by nine is negative 27 negative three multiplied by zero is zero, negative three multiplied by 11 is negative 33. Close that matrix next, my second matrix will be multiplied each element by five. So starting in the top left five, multiplied by negative 12 is negative 60 five. Multiplied by six is 30 five, multiplied by nine is 45 5, multiplied by zero is zero. Now that my new matrices have been created, I can add them together. Recall that when you add matrices, they have to have the same dimensions and you add the corresponding parts. So 15 would be added to negative 60 which would be negative 45 in the top left corner, negative 27 would be added to 30 which would give us a positive three in the top right corner. Zero plus 45 is 45 in the bottom left corner, negative 33 plus zero is negative 33 in the bottom right hand corner. This is our answer matrix. The top row is negative 45 3. The bottom row is 45 negative 33 and that matches answer choice B have a nice day.

Let and . Find each of the following. See Examples 2 –4.
2A + 4B

Key Concepts

Matrix Addition and Scalar Multiplication

Matrix Dimensions and Compatibility

Order of Operations in Matrix Expressions

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