Question

If p, q, r are 3 real numbers satisfying the matrix equation , $[ p \ q \ r ] \begin{bmatrix}3&4&1\\\ 3&2&3\\\ 2&0&2\end{bmatrix} = \begin{bmatrix}3&0&1\end{bmatrix}$ then 2p + q - r equals :

• A. -3
• B. -1
• C. 4
• D. 2

Answer 1

Answer: (A)

-3

Answer 2

Given $\begin{bmatrix}p&q&r\end{bmatrix} \begin{bmatrix}3&4&1\\\ 3&2&3\\\ 2&0&2\end{bmatrix} = \begin{bmatrix}3&0&1\end{bmatrix}$ $\Rightarrow \begin{bmatrix}3p + 3q + 2r&4p + 2q&p + 3q + 2r\end{bmatrix} = \begin{bmatrix}3&0&1\end{bmatrix}$ $\Rightarrow \ 3p + 3q + 2r = 3$ ...(i) $4p + 2q = 0 \ \Rightarrow \ q = - 2p$ ...(ii) $p + 3q + 2r = 1$ ...(iii) On solving (i), (ii) and (iii), we get p = 1, q = - 2, r = 3 $\therefore$ 2p + q - r = 2(1) + (- 2) - (3) = - 3.