Explanation
To determine if two matrices can be multiplied and to find the dimensions of the resulting matrix, we look at their individual dimensions step-by-step:
Step 1: Check compatibility for multiplication Matrix multiplication AB is only defined if the number of columns in the first matrix (A) matches the number of rows in the second matrix (B).
Dimensions of A: 3×4 (3 rows, 4 columns)
Dimensions of B: 4×3 (4 rows, 3 columns)
Since the inner dimensions match (4=4), the multiplication AB is completely valid and possible.
Step 2: Determine the size of the product matrix The resulting matrix inherits its number of rows from the first matrix and its number of columns from the second matrix. This rule can be visually represented by looking at the outer dimensions:
Size of AB=(Rows of A)×(Columns of B)
Substituting the given matrix dimensions:
Size of AB=3×3
