Question

Consider the system of equations $2x+P^{2}y+6z=8$ , $x+2y+2qz=5$ and $x+y+3z=4$

• A. Given system has unique solution for $P\neq \pm\sqrt{2}$ and $q=\frac{3}{2}$
• B. Given system has no solution for $P=\pm\sqrt{2}$ and $q=\frac{3}{2}$
• C. Given system has infinite solution for $P=\pm\sqrt{2}$ and $q\in R$
• D. None of these

Answer 1

Answer: (C)

$D=\begin{vmatrix} 2 & p^{2} & 6 \\ 1 & 2 & 2q \\ 1 & 1 & 3 \end{vmatrix}=\left(p^{2} - 2\right)\left(\right.2q-3\left.\right)$
$D_{2}=0$
$D_{1}=\left(p^{2} - 2\right)\left(\right.8q-15\left.\right),D_{3}=\left(P^{2} - 2\right)$