Let's consider an example system of linear equations.
2x + 3y - 2z= 3 & (I) 2x + 2y + 2z = 6 & (II) 12x - 3y + 5z = 14 & (III)
Any system of linear equations can be written as a matrix. The entries of the matrix are the coefficients of the variables from the system. We make a vertical line to represent the equal signs. The numbers on the right-hand side of this line are the constants. Let's rewrite the system of equations as a matrix.
2x+ 3y - 2z= 3 2x+ 2y+ 2z= 6 12x - 3y+ 5z= 14
⇕
[
ccc|c
2 & 3 & - 2 & 3
2 & 2 & 2 & 6
12 & - 3 & 5 & 14
]
This type of matrix is called an augmented matrix. The array that can be used to solve a system of linear equations is the matrix that contains only the constants.
[
c
3
6
14
]
It is called the constant matrix. We can fill in the blank.
