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

Question

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

Aicharya · Accepted Answer

Given $ \begin{aligned} & {\left[\begin{array}{lll} p & q & r \end{array}ight]\left[\begin{array}{lll} 3 & 4 & 1 \ 3 & 2 & 3 \ 2 & 0 & 2 \end{array}ight]=\left[\begin{array}{lll} 3 & 0 & 1 \end{array}ight]} \ & \Rightarrow\left[\begin{array}{lll} 3 p+3 q+2 r & 4 p+2 q & p+3 q+2 r \end{array}ight]=\left[\begin{array}{lll} 3 & 0 & 1 \end{array}ight] \ & \Rightarrow 3 p+3 q+2 r=3 \ & 4 p+2 q=0 \Rightarrow q=-2 p \ & p+3 q+2 r=1 \ & \end{aligned} $ $p=1, q=-2, r=3$ $	herefore 2 p+q-r=2(1)+(-2)-(3)=-3$

If $p, q, r$ are 3 real numbers satisfying the matrix equation, $[p q r]\left[\begin{array}{lll}3 & 4 & 1 \\…

Solution