Representing a linear system as a matrix  Matrices
Representing a linear system as a matrix
In this lesson, we will learn how to turn a linear system into a matrix. What we do is draw a big bracket, take all the coefficients of each term and write it in, draw a vertical line, write all the numbers after the equal sign, and end it with another big bracket. Terms that do not seem to have a coefficient actually do. For example the term y can be rewritten to 1*y, and so the coefficient of this will be 1. Notice that when you turn it into a matrix, all the variables disappear since the most important part are the numbers.
Lessons
Notes:
We can represent a linear system as a matrix. For example, the linear system
$1x+2y+3z=4$
$5x+6y+7z=8$
$9x+10y+11z=12$
can be represented as the matrix:
where $x,y,z$ are variables and the vertical line represents the equal sign for each linear equation. We see all the $x,y,z$’s disappear, and we take all the coefficients and the numbers after the equal sign.

2.
Representing a linear system as a matrix
Represent each linear system as a matrix: 
3.
Representing a matrix as a linear system
Represent each matrix as a linear system: