Question

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

• A. unique
• B. two
• C. 0
• D. infinite

Answer 1

Answer: (D)

infinite

The given system of equations can be written as $AX=O$
where $A=\left[\begin{array}{ccc}1& 2& -3\\ 2& -1& 2\\ 1& 7& -11\end{array}\right]$, $X=\left[\begin{array}{c}x\\ y\\ z\end{array}\right],O=\left[\begin{array}{c}0\\ 0\\ 0\end{array}\right]$
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 solution