Question

The solution set of $\left|\begin{array}{ccc}a& a& x\\ m& m& m\\ b& x& b\end{array}\right|=0$ is

• A. {a,b}
• B. {0,b}
• C. {m,a}
• D. {a,0}

Answer 1

Answer: (A)

{a,b}

$\left|\begin{array}{ccc}a& a& x\\ m& m& m\\ b& x& b\end{array}\right|=0$
Taking $m$ common from second row, we get,
$\left|\begin{array}{ccc}a& a& x\\ 1& 1& 1\\ b& x& b\end{array}\right|=0$
Now, using $C_1=C_1-C_2$
$\left|\begin{array}{ccc}0& a& x\\ 0& 1& 1\\ b-x& x& b\end{array}\right|=0$
Expanding along first row,
$(b-x)(a-x)=0\Rightarrow x=a,b$