Question

The system of equations $x+2y-3z=0,2x-y+2z=0,x+7y-11z=0$ has

• A. unique solution
• B. two solutions
• C. no solution
• D. infinite solutions

Answer 1

The correct option is D infinite solutions

The given system of equations can be written as $AX=0$

$\text{where A}=\left[\begin{array}{ccc}1& 2& -3\\ 2& -1& 2\\ 1& 7& -11\end{array}\right],X=\left[\begin{array}{c}x\\ y\\ z\end{array}\right],O=\left[\begin{array}{c}0\\ 0\\ 0\end{array}\right]$

$\text{Here},|A|=\left|\begin{array}{ccc}1& 2& -3\\ 2& -1& 2\\ 1& 7& -11\end{array}\right|$

$|A|=-3+48-45=0$
$A$ is singular.
So, the system has infinitely many solutions