Problem 79 - College Algebra

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 - two matrices with the same dimensions but an unequal number of rows and columns could be added but not multiplied.

Step 1: Analyze the statement for matrix addition

Here, it's shared that they are working with two matrices that can be added. For matrix addition to be possible, the two matrices must have the same dimensions - that is, the same number of rows and columns.

Step 2: Analyze the statement for matrix multiplication

On the other hand, for matrix multiplication to be possible, the number of columns in the first matrix must be equal to the number of rows in the second matrix.

Step 3: Determine if the statement makes sense

The two matrices can be added, meaning they have the same dimensions. However, the two matrices can't be multiplied, implying that the number of columns in the first matrix isn't equal to the number of rows in the second matrix. Therefore, it makes sense that two matrices of the same size, but that are not square matrices (non-equal number of rows and columns), could be added but not multiplied.