Question

If $\left|\begin{array}{ccc}a& a& x\\ m& m& m\\ b& x& b\end{array}\right|=0$, then $x$ may be equal to

• A. $a$
• B. $b$
• C. $a+b$
• D. $m$

Answer 1

Answer: (A), (B)

The correct options are
A $a$
B $b$

If $x=a$
$\left|\begin{array}{ccc}a& a& x\\ m& m& m\\ b& x& b\end{array}\right|=\left|\begin{array}{ccc}a& a& a\\ m& m& m\\ b& a& b\end{array}\right|=am\left|\begin{array}{ccc}1& 1& 1\\ 1& 1& 1\\ b& a& b\end{array}\right|=0$
And if $x=b$
$\left|\begin{array}{ccc}a& a& x\\ m& m& m\\ b& x& b\end{array}\right|=\left|\begin{array}{ccc}a& a& b\\ m& m& m\\ b& b& b\end{array}\right|=bm\left|\begin{array}{ccc}a& a& b\\ 1& 1& 1\\ 1& 1& 1\end{array}\right|=0$