Question

The system of equation $\left(\sin \alpha \right)x+2z=0,\left(\cos \alpha \right)x+\left(\sin \alpha \right)y=0;\left(\cos \alpha \right)y+2z=a$ has (where a and $\alpha$ are constants)

• A. No solution
• B. A unique solution
• C. Infinitely many solution
• D. Finitely many solution

Answer 1

The correct option is B A unique solution

Given equations are,

$\left(sin\alpha \right)x+2z=0,\left(cos\alpha \right)x+\left(sin\alpha \right)y=0,\left(cos\alpha \right)y+2z=a$

Then,

$\Delta =\left|\begin{array}{ccc}sin\alpha & 0& 2\\ cos\alpha & sin\alpha 0& \\ 0& cos\alpha & 2\end{array}\right|$

$=sin\alpha (2sina\alpha -0)+2(co{s}^2\alpha -0)$

$=2(si{n}^2\alpha +co{s}^2\alpha )$

$=2$

Hence $\Delta \ne 0$ So given system of euation has unique solution.