Introduction to Linear Algebra

"Algebraic Method" of solving linear equations using Matrices.

Consider the following system:

3x1 + 2x2 - x3 + x4 =  -1

2x1          - x3 + 2x4 = 0

3x1 + x2 - 2x3 + 5x4 = -1

Augmented Matrix :

[ 3 2 -1 1 | -1 ]

[ 2 0 -1 2 |   0 ]

[ 3 1   2 5 |   2 ]

Coefficient Matrix :

[ 3 2 -1 1 ]

[ 2 0 -1 2 ]

[ 3 1   2 5 ]

Constant Matrix :

[  -1 ]

[   0 ]

[   2 ]