Answer
please see work step-by-step
Work Step by Step
Matrices provide us with a shortened way of writing (and solving) linear equations.
$\left\{\begin{array}{lllll}
a_{11}x_{1} & +a_{12}x_{2} & +... & +a_{1n}x_{n} & =b1\\
a_{21}x_{2} & +a_{22}x_{2} & +.... & +a_{2n}x_{3} & =b_{2}\\
... & ... & +... & ... & =...\\
a_{m1}x_{1} & +a_{m2}x_2 & +... & +a_{mn}x_{n } & = b_n
\end{array}\right.$
The augmented matrix has as many rows as there are equations.
It has a vertical bar separating the columns of the matrix into two groups:
- to the left, coefficients of each variable,
- to the right, the constants.
The augmented matrix has form
$\left[\begin{array}{llllll}
a_{11} & a_{12} & ... & a_{1n} & | & b_{1}\\
a_{21} & a_{22} & .... & a_{2n} & | & b_{2}\\
... & ... & ... & ... & | & ...\\
a_{m1} & a_{m2} & ... & a_{mn}& | & b_{n}
\end{array}\right]$,
