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The sub-indices in the variable names X, Y, and Z, determine to which
equation system they refer to. To solve this expanded system we use the
following procedure, in RPN mode,
[[14,9,-2],[2,-5,2],[5,19,12]]
`
[[1,2,3],[3,-2,1],[4,2,-1]]
`/
The result of this operation is:
Gaussian and Gauss-Jordan elimination
Gaussian elimination is a procedure by which the square matrix of coefficients
belonging to a system of n linear equations in n unknowns is reduced to an
upper-triangular matrix (
echelon form
) through a series of row operations.
This procedure is known as
forward elimination
. The reduction of the
coefficient matrix to an upper-triangular form allows for the solution of all
n
unknowns, utilizing only one equation at a time, in a procedure known as
backward substitution
.
Example of Gaussian elimination using equations
To illustrate the Gaussian elimination procedure we will use the following
system of 3 equations in 3 unknowns:
2X +4Y+6Z = 14,
3X -2Y+ Z = -3,
4X +2Y -Z = -4.
We can store these equations in the calculator in variables E1, E2, and E3,
respectively, as shown below. For backup purposes, a list containing the
three equations was also created and stored into variable EQS. This way, if a
mistake is made, the equations will still be available to the user.
.
2
1
3
1
5
2
2
2
1
−
−
=
X
