Question

Find the solution of the following system of linear equations.

$\left[\begin{array}{ccc}-1& 2& 1\\ 3& -1& 2\\ 0& 1& 1\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]$

Answer 1

Given

$\underset{\begin{array}{c}\downarrow \\ A\end{array}}{\left[\begin{array}{ccc}-1& 2& 1\\ 3& -1& 2\\ 0& 1& 1\end{array}\right]}\underset{\begin{array}{c}\downarrow \\ X\end{array}}{\left[\begin{array}{c}x\\ y\\ z\end{array}\right]}=\underset{\begin{array}{c}\downarrow \\ B\end{array}}{\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]}$

$\therefore X=A^{-1}B$ ........... $\left(1\right)$

$|A|=\left|\begin{array}{ccc}-1& 2& 1\\ 3& -1& 2\\ 0& 1& 1\end{array}\right|=-1(-1-2)-2\left(3\right)+1\left(3\right)$

$\because |A|=0⟹A^{-1}$ does not exist.

Hence, the given system of equation cannot be solved