Vector: Matrix where n is 1, so there is only one row

A matrix is made up of rows and columns like a table

Rows: Horizontal, has “m” amount of rows

Columns: Vertical, has “n” amount of columns

Order of matrix: rows*columns
When m = n the matrix is said to be square

Matrices can be used to solve systems of equations (Gaussian Elimination):

A step by step of solving with system of equations:

Identity Matrix:

How a matrix can be simplified:

Matrix Operations:

Matrices have to be in the SAME order to be added or subtracted, and each component is added with the corresponding component in the other matrix

The order of the matrices in multiplication does matter and can give radically different answers
You also can’t multiply matrices of different sizes

AB and BA are both equal to I

How to find an easy inverse of a matrix:

The determinant: The volume of the scaling factor of the linear transformation.

Example of Cramer’s Rule:

Components in matrices:

Zero Matrix: A matrix where every component is 0