Question

Given $A=\left[\begin{array}{cccc}12& -6& 18& 30\\ 0& 12& 6& -18\\ 0& 0& -6& -12\end{array}\right],B=\left[\begin{array}{cccc}6& -3& 9& 15\\ 0& 6& 3& -9\\ 0& 0& -3& -6\end{array}\right]$ and $C=\left[\begin{array}{cccc}2& -1& 3& 5\\ 0& 2& 1& -3\\ 0& 0& -1& -2\end{array}\right],$ then which of the following is not correct

• A. $A=3B$
• B. $A=6C$
• C. $B=3C$
• D. $A=2B$

Answer 1

The correct option is A $A=3B$

On multiplying by a scalar $2$ to matrix $B$
we get $2B=A\cdots \left(i\right)$
Similarly, if we multiply by $6$ in matrix $C$
we get, $6C=A\cdots \left(ii\right)$
From $\left(i\right)$ and $\left(ii\right)$
$\Rightarrow B=3C$