Problem 80 - 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 multiplied but not added.

Step-by-Step Solution

Answer

The statement makes sense considering the fundamental rules of matrix addition and multiplication. If the dimensions (number of rows and columns) of two matrices are different but the second dimension of the first matrix equals the first dimension of the second, they can be multiplied but not added.

Step 1: Understanding Matrix Addition

Two matrices can be added or subtracted only if they are of the same size, i.e., they must have the same number of rows and the same number of columns.

Step 2: Understanding Matrix Multiplication

Two matrices can be multiplied if and only if the number of columns in the first matrix equals the number of rows in the second matrix.

Step 3: Apply the Above Understandings to the Original Statement

When the statement 'I'm working with two matrices that can be multiplied but not added' is evaluated using the aforementioned rules, it is found to make sense. This situation can happen if the two matrices have different dimensions but satisfy the condition for multiplication. For instance, a 3x2 matrix can be multiplied with a 2x3 matrix but they cannot be added as they don't have the same dimensions.