MATRIX

BASIC MATRIX

i - rows (position in the jth column), m - number of rows

j - columns (position in the ith row), n - number of columns

AUGMENTED MATRIX

An Augmented matrix of some system of equations has the form (m x (n+1)):

THE SYSTEM REDUCE - ROW REDUCE

By treating every row as one equation of a linear system, we can use the elimination method to get the simpler results:

(1) Add 2 times the first row to the second and add the first row to the third.

(2) Multiply the fourth row by -1/2 and interchange it with the second row.

(3) Add -3 times the second row to the third and -4 times the second to the fourth.

(4) Multiply the third row by -1/3 and add it to the fourth.

DETERMINANTS

COFACTOR

TRANSPOSE MATRIX

INVERSE

Example 1

Example 2

The other way to find an inverse of a matrix would be to place another matrix next to the original one, for i = j, a = 1 else a = 0.

The goal is to get the first matrix into this form, using basic row operations. The same operations done on the first matrix should be done on the other, with the same values ussed.

At the end, the other matrix becomes the inverse matrix of the first matrix at the start.

CRAMER'S RULE

MATRIX MULTIPLICATION

Example 1