Linear Algebra Lecture 1 - 7

give the elementary row operation

Consistent vs Inconsistent system

Definition Echelon Form

Definition Reduced Echelon Form

Basic vs Free variables

Give the process of solving a system of equations

definition Linear Combination

definition Vector Equation

definition span

definition Matrix-Vector product

calculation rules for a matrix - vector product

list the equivalent different equations (with matrices & vectors)

list the equivalent ways to find solutions (with matrices & vectors)

Definition Homogeneous System

structure of the solution set of a consistent, non-homogeneous system

Definition Linear Independence

Definition Linear Dependence

Definition Linear Transformation

*Note: a Matrix Transformation is something of the result Ax

Definition Standard Matrix

Give the linear transformation that does a rotation around the origin

List the special types of matrices

Give the calculation rules for matrices

*Note: AB does not equal BA!!

How does matrix multiplication work?

Link matrix multiplication and composite linear transformations

Properties of Matrix Multiplication

Transpose of a Matrix

Transpose calculation rules

Definition inverse of a matrix

How to solve linear systems with inverse matrices?

Properties of inverse matrices

How to find the inverse of a matrix

List the invertible matrix theorem (give 5 equivalent statements)

Definition Invertible Linear Transformations

Quite obvious since Linear Transformation are basically a type of matrix multiplication