Let's begin our investigation by looking at matrix multiplication. This review will provide background for understanding content in the rest of this section.

To multiply a row matrix by a column matrix, you work in this way:

To multiply matrix A by matrix B, the elements of A (in a row) are multiplied by the elements of B (in a column). Then the results are added. The resulting matrix, AB, is a 1x1 matrix with the value 70.

The same pattern is followed if you have more than a single row or column. Again, each element in the row of one matrix is multiplied by the corresponding element in the column of another matrix.

The next step: This continues for all the elements of the matrix.

Here is the case of a 3x3 matrix multiplied by itself:

Many calculators have a matrix algebra capacity, and calculations with matrices can also be done in most spreadsheet programs. If you have access to such a tool, please work with it now. You may need to refer to program- or calculator-specific documentation for information about entering matrices.

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