Practice with Dimensions

Column matrices and row matrices are a special case of rectangular matrices, so the rule covers them, as well. You may wish to practice with the following. Determine the dimensions of the product of each pair of matrices. Click on the button to check your answer.

Matrix	Matrix	Result	Matrix	Matrix	Result
4 × 3	3 × 2		3 × 2	2 × 2
2 × 3	2 × 3		4 × 3	3 × 1
3 × 5	5 × 1		3 × 1	1 × 4

Check the dimensions of the result before you do the arithmetic. For example, the last product (in the table) is a bit odd, and it is easy to get mixed up without knowing what the result should look like.