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The diagonal matrix that results from a Gauss-Jordan elimination is called a
row-reduced echelon form. Function RREF
( Row-Reduced Echelon Form) The
result of this function call is to produce the row-reduced echelon form so that the
matrix of coefficients is reduced to an identity matrix. The extra column in the
augmented matrix will contain the solution to the system of equations.
As an example, we show the result of applying function RREF to matrix AAUG
in ALG mode:
The result is final augmented matrix resulting from a Gauss-Jordan elimination
without pivoting.
A row-reduced echelon form for an augmented matrix can be obtained by
using function
rref. This function produces a list of the pivots and an equivalent
matrix in row-reduced echelon form so that the matrix of coefficients is reduced
to a diagonal matrix.
For example, for matrix AAUG, function rref produces the following result:
The second screen above is obtained by activating the line editor (press ˜).
The result shows pivots of 3, 1, 4, 1, 5, and 2, and a reduced diagonal matrix.
Function SYST2MAT
This function converts a system of linear equations into its augmented matrix
equivalent. The following example is available in the help facility of the
calculator: