Solution of Linear Equations by Gaussian Elimination and Back-Substitution
Solution of Linear Equations by Gaussian Elimination and Back-Substitution
Initialise
Clear the workspace and load Linear Algebra package
restart;
with(LinearAlgebra):
If you want practice at hand calculation you should use the worksheet “Interactive Gaussian Elimination” (see Menu)
Enter the matrix of coefficients and right-hand side vector
You may edit the following statements or use the matrix and vector pallettes to enter new data ( see View, Palettes)
> b:=<<15, 7, 6>>;
Form the augmented matrix and solve
The Maple routine GaussianElimination requires the augmented matrix A|b as input.
In this worksheet this matrix is called Ab and is formed using
Ab:=
The row echelon form H|c (here called Hc) of Ab is computed by GaussianElimination.
(For a square system of equations the row echelon form of A is upper triangular )
Note that the Maple function GaussianElimination performs a systematic version of the idea of elementary row operations:
(i) Multiples of R1 are subtracted from R2, R3 . . Rn to reduce the elements below the leading diagonal in the first column to zero.
(ii) In the resulting system multiples of R2 are subtracted from R3, R4 . . Rn to reduce the elements below the leading diagonal in the second column to zero.
(iii) This process