Question

If \(M\) is a \(3 \times 3\) matrix such that \((012) M=(100),(345) M=(010)\), then \((678) M\) is equal to
(A) \((21-2)\)
(B) \(\left(\begin{array}{lll}0 & 0 & 1\end{array}\right)\)
(C) \((-120)\)
(D) \((9108)\)

Answer 1

Ans: (C)
Hint: \((012) m=\left(\begin{array}{lll}1 & 0 & 0\end{array}\right) \quad\) (i)
\((345) \mathrm{m}=\left(\begin{array}{lll}0 & 1 & 0\end{array}\right)\)
(6 810 ) \(m=\left(\begin{array}{lll}0 & 2 & 0\end{array}\right)\) (ii)
(ii) - (i)
\(\left(\begin{array}{lll}6 & 8 & 10\end{array}\right) m-\left(\begin{array}{lll}0 & 1 & 2\end{array}\right) m=\left(\begin{array}{lll}0 & 2 & 0\end{array}\right)-\left(\begin{array}{lll}1 & 0 & 0\end{array}\right)\)
\(\Rightarrow(678) m=(-120)\)