Question

Matrix C has the dimensions 7 X 2 and Matrix D has the dimensions 2 X 7. Determine the dimensions of the matrix CD, if it is possible. Explain why if it is not.

A. Matrix CD would have the dimensions 2 X 2

B. Matrix CD would have the dimensions 2 X 7

C. Matrix CD would have the dimensions 7 X 7

D. These matrices cannot be multiplied because their dimensions don't align.

Answer 1

Matrix C (7 X 2) can be multiplied by Matrix D (2 X 7), resulting in a matrix CD with dimensions 7 X 7.

Step-by-step explanation:

When it comes to matrix multiplication, the inner dimensions of the matrices must match for the multiplication to be possible. This means that a matrix with dimensions 7 X 2 (Matrix C) can be multiplied by a matrix with dimensions 2 X 7 (Matrix D) since the inner numbers (2 and 2) are equal. The dimensions of the resulting matrix CD will be determined by the outer numbers, which are 7 from Matrix C and 7 from Matrix D.

Therefore, the dimensions of matrix CD will be 7 X 7.