What is Linear Algebra and What do i know about it?

Linear Algebra is the branch of mathematics concerning Vector spaces and linear mappings between such spaces. It is the study of lines, planes, and subspaces and their intersections using algebra.

List of Linear Algebra Topics:

Linear Equations
Matrices
Matrix Decompositions
Relations
Computations
Vector Spaces

What do i know about Linear equations?
        - Linear equations are collectively know as a system. Systems are composed of linear equations with the same set of variables. For example:









The above system is a system of three equations in three variables x,y, and z. A solution to a linear system is an assignment of numbers to the variables such that all equations are simultaneously satisfied.The solution to the above equation is x=1, y=-2, z=-2. 

What do i know about Matrices?
       -a matrix is a rectangular array of numbers, symbols, or expressions arranged in m rows and n columns. The individual items in a matrix are called entries. A matrix that has equal number of rows and columns (m=n) is called a square matrix. Matrices are linear systems and are solved using elementary row operations.