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.

Example :

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 another

GAUSSIAN ELIMINATION :

Transform rows until each has only 1 variable.

This means "diagonal" elements 1, all other numbers except right column are 0.

TRIANGULARIZATION :

Transform equations until lower triangle is all zeroes, then apply "back-substitution".

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