Lesson 26 - Learning Goals
26.1 Learn what is meant by Linear Algebra
26.2 Learn the process to solve a set of Linear equations
26.3 Learn how to implement Gaussian Elimination in FORTRAN
A system of n linear equations
in n unknowns has (hopefully) one solution.
5x + 3y - z = 8
x - y + 2z = 5
2x - 3y + 4z = 8
TRANSFORMS PRESERVING SOLUTION
Exchange two rows
Multiply a row by a constant
Add a multiple of one row to
GAUSSIAN ELIMINATION :
Transform rows until each has only 1 variable.
This means "diagonal"
elements 1, all other numbers except right column are 0.
Transform equations until lower
triangle is all zeroes, then apply "back-substitution".
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