The matrix cap r is equal to the 2 by 1 column matrix 12 4 represents the length of 12 in. and the width of 4 in. of a rectangle. If matrix multiplication is used to double the length and width of the rectangle, which rectangle represents the result of the matrix multiplication?
Answer
A
Image with description A 12 in. by 8 in. rectangle
B
Image with description A 12 in. by 4 in. rectangle
C
Image with description A 24 in. by 8 in. rectangle
D
Image with description A 24 in. by 4 in. rectangle
Explanation
The column matrix contains the rectangle’s length and width: 12 in. and 4 in. Doubling both dimensions means multiplying each entry by 2, giving a length of 2 × 12 = 24 in. and a width of 2 × 4 = 8 in. So the result is the 24 in. by 8 in. rectangle.
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