Question

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

• A. -3
• B. -1
• C. 4
• D. 2

Answer 1

Answer: (A)

Given
$\left[\begin{array}{ccc}p& q& r\end{array}\right]\left[\begin{array}{ccc}3& 4& 1\\ 3& 2& 3\\ 2& 0& 2\end{array}\right]=\left[\begin{array}{ccc}3& 0& 1\end{array}\right]$
$\Rightarrow \left[\begin{array}{ccc}3p+3q+2r& 4p+2q& p+3q+2r\end{array}\right]=\left[\begin{array}{ccc}3& 0& 1\end{array}\right]$
$\Rightarrow 3p+3q+2r=3$ ...(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.