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RepresentationSession 05 OverviewTab atab btab ctab dtab eReference
Part A

Observing Representation
  Review Matrix Multiplication | Taxicabs | Student Work | Student Work Reflection #1 | Matrix Approach | Interpreting Matrices | Student Work Reflection #2 | Classroom Practice | Observe a Classroom | Your Journal


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:

Matrix Brackets

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.

Matrix Brackets 2a

The next step:

Matrix Brackets 2b

This continues for all the elements of the matrix.

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

3x3 matrix

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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