Let $A=\left[\begin{array}{ccc}b^2+c^2 & a^2 & a^2 \ b^2 & c^2+a^2 & b^2 \ c^2 & c^2 & a^2+b^2\end{array} ight]$. If $a=\sin \frac{\pi}{6}, b=\cos \frac{\pi}{4}$ and $c=\cot \frac{\pi}{2}$, then $A$ is

Question

Let $A=\left[\begin{array}{ccc}b^2+c^2 & a^2 & a^2 \ b^2 & c^2+a^2 & b^2 \ c^2 & c^2 & a^2+b^2\end{array}ight]$. If $a=\sin \frac{\pi}{6}, b=\cos \frac{\pi}{4}$ and $c=\cot \frac{\pi}{2}$, then $A$ is

Aicharya · Accepted Answer

$ \begin{aligned} & 	ext { Given, } a=\sin \frac{\pi}{6}=\frac{1}{2}, b=\cos \frac{\pi}{4}=\frac{1}{\sqrt{2}}, \ & c=\cot \frac{\pi}{2}=0 \ & \because \quad|A|=\left|\begin{array}{lll} \frac{1}{2} & \frac{1}{4} & \frac{1}{4} \ \frac{1}{2} & \frac{1}{4} & \frac{1}{2} \ 0 & 0 & \frac{3}{4} \end{array}ight| . \end{aligned} $ Here, $c_1=2 c_2$ $ 	herefore \quad|A|=0 $ $	herefore A$ is singular matrix

Let $A=\left[\begin{array}{ccc}b^2+c^2 & a^2 & a^2 \\ b^2 & c^2+a^2 & b^2 \\ c^2 & c^2 &…

Solution