Matrices

On a test, you are expected to do the arithmetic necessary to put matrices in reduced row echelon form for a 2 by 3 matrix by hand (see example below). For larger matrices, you are expected to use your calculator.  You are also expected to interpret the numbers your calculator finds,

1. giving the unique solution if there is one,
2. giving the form of the solutions if there are an infinite number of them, or
3. recognizing that there are no solutions.

To use the reduced row echelon method of section 9.3, enter the augmented matrix in your calculator as described on the handout, except that the number of columns must be adjusted for the augmented part of the matrix. Use the [MATRX] key, highlight the MATH header, scroll down to 'rref(' by repeatedly pressing the down arrow key, and press [ENTER]. Then use the [MATRX] key again, highlight the NAMES header, and press the number corresponding to the name of the matrix you want. Press [ENTER] and the reduced row echelon form of the matrix appears. You may need to use the right arrow key to see some of the entries to the right of the matrix. The ugly arithmetic is done and you need only to interpret the results.

Here is an example of how to solve a matrix by hand.