Question

Given that $A =\begin{bmatrix}3&2\\ 5&7\\ 8&9\end{bmatrix}, B = \begin{bmatrix}1&9\\ 0&3\\ 4&10\end{bmatrix}$ and $X = \begin{bmatrix}6&29\\ 5&16\\ 20&39\end{bmatrix}$ and if $2 A +6 B = kX$, then the value of $k$ is

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

Answer: (A)

$\because 2 A +6 B = kX$
$\therefore 2\begin{bmatrix}3&2\\ 5&7\\ 8&9\end{bmatrix} +6\begin{bmatrix}1&9\\ 0&3\\ 4&10\end{bmatrix}=k \begin{bmatrix}6&29\\ 5&16\\ 20&39\end{bmatrix}$
or $\begin{bmatrix}6&4\\ 10&14\\ 16&18\end{bmatrix} +\begin{bmatrix}6&54\\ 0&18\\ 24&60\end{bmatrix}=k \begin{bmatrix}6&29\\ 5&16\\ 20&39\end{bmatrix}$
or $\begin{bmatrix}12&58\\ 10&32\\ 40&78\end{bmatrix}=k\begin{bmatrix}6&29\\ 5&16\\ 20&39\end{bmatrix}$
or $2\begin{bmatrix}6&29\\ 5&16\\ 20&39\end{bmatrix} =k\begin{bmatrix}6&29\\ 5&16\\ 20&39\end{bmatrix} \therefore k=2$