Multiplying Matrices
We can only multiply matrices if the number of columns in the first matrix is the same as the number of rows in the second matrix.
Multiplying a 2 × 3 matrix by a 3 × 4 matrix is possible and it gives a 2 × 4 matrix as an answer.
Multiplying a 7 × 1 matrix by a 1 × 2 matrix is okay; it gives a 7 × 2 matrix
A 4 × 3 matrix times a 2 × 3 matrix is NOT possible.
How to Multiply 2 Matrices?
Step 1: We multiply and add the elements as follows. We work across the 1st row of the first matrix, multiplying down the 1st column of the second matrix, element by element. We add the resulting products.
Step 2: We do a similar process for the 1st row of the first matrix and the 2nd column of the second matrix.
Step 3: Now for the 2nd row of the first matrix and the 1st column of the second matrix.
Step 4: Do the 2nd row of the first matrix and the 2nd column of the second matrix.
Find out more about multiplying matrices below.
Practice: Answer the following exercises by finding the product of two matrices.