Rules of matrix multiplication

1. The matrix multiplication must be defined. The number of columns in the first matrix must equal the number or rows in the second matrix. This can be observed through inspection in the case of both of the matrix orders being written out sideby side– the two middle numbers must equal to each other.
2. The order of the product matrix is specific. The product matrix will have the same number of rows as the first matrix, and the same number of columns as the second matrix. Again, the order of the product matrix can be determined through inspection– if both of the matrix orders are written out, the order of the product matrix is equal to the outside values. That is, if A is of the order (a x b) and B is in the order (b x c), the order of the product matrix is (a x c).

Determining matrix products

In Further Math, it is highly recommended that the multiplication of matrices be done by technology. This is because the manual way is tedious and hence prone to errors. However, to find the product of two matrices by hand, the following method is used:

1. Determine whether the matrix product is defined.
2. Find its order.
3. Multiply each element in the row by the corresponding element in the column matrix.
4. Add the results.
5. Write down your answers.

Application

See also:

• Using matrices to represent information
• Addition, subtraction and scalar multiplication of matrices