Operations with Matrices

Notation and definiton

Dimensions

Inner/outer matrix product

Definition the matrix multiplication of the matrix form of the SLE

Multiply a matrix to a column vector

Multiply a matrix into another matrix as a linear combinations of the columns

Multiply a row to a matrix

Multiply AB as a linear combinations of rows of B

Big augmented matrix

Performing gauss jordan elimination of the augmented matrix multiple systems of linear equations

Defining the inverse matrices

Brief discussions on invertibility of matrices

Problem of finding the inverse as solving systems of linear equations

Solving multiple systems at one to obtain the inverse

Elemetary row operations as elementary matrices

Inverses of elementary matrices