Problem 79 - Algebra and Trigonometry

Question

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I'm working with two matrices that can be added but not multiplied.

Step-by-Step Solution

Answer

The statement makes sense because while matrix addition requires similarity in dimension of matrices, matrix multiplication needs the number of columns in the first matrix to match the number of rows in the second matrix.

Step 1: Understanding Matrix Addition

Matrix addition is only possible when the two matrices have the same dimensions. That is, they must have the same number of rows and the same number of columns.

Step 2: Understanding Matrix Multiplication

Matrix multiplication, unlike addition, does not require the two matrices to have the same dimensions. Instead, the number of columns in the first matrix must be equal to the number of rows in the second matrix.

Step 3: Evaluating the Statement

If two matrices can be added, that means they have the same dimensions. But this doesn't necessarily mean they can be multiplied, because multiplication requires the number of columns in the first matrix to match the number of rows in the second. Hence, the statement makes sense.