Q. 12

Write the system of equations corresponding to the given augmented matrix.

$[\begin{array}{rrrr} 1 & 2 & 5 & - 2 \\ 5 & 0 & - 3 & 8 \\ 2 & - 1 & 0 & 0 \end{array}]$

Verified

Answer

The system of equations is $\{\begin{aligned} x + 2 y + 5 z & = - 2 \\ 5 x - 3 z & = 8 \\ 2 x - y & = 0 \end{aligned}$

1Step 1. Given information

The given augmented matrix is $[\begin{array}{rrrr} 1 & 2 & 5 & - 2 \\ 5 & 0 & - 3 & 8 \\ 2 & - 1 & 0 & 0 \end{array}]$

2Step 2. Convert augmented matrix into the system of equations.

If the two variables are $x$ and $y$ , then the system of equations is

$\{\begin{aligned} x + 2 y + 5 z & = - 2 \\ 5 x - 3 z & = 8 \\ 2 x - y & = 0 \end{aligned}$