Question

if the matrix (cosx,sinx,2)(sinx,cosx,-3)(0,0,1)is singular find the general value of x​

Answer 1

$\textbf{Given:}$

$\textsf{Matrix is}$

$\mathsf{\left(\begin{array}{ccc}cosx&sinx&2\\0&2&1\\sinx&cosx&-3\\0&0&1\end{array}\right)\;is\;singular}$

$\textbf{To find:}$

$\textsf{General value of x}$

$\textbf{Solution:}$

$\mathsf{Since\;\left(\begin{array}{ccc}cosx&sinx&2\\0&2&1\\sinx&cosx&-3\\0&0&1\end{array}\right)\;is\;singular,}$

$\mathsf{\left|\begin{array}{ccc}cosx&sinx&2\\0&2&1\\sinx&cosx&-3\\0&0&1\end{array}\right|=0}$

$\textsf{Expanding along the first row, we get}$

$\mathsf{cosx(cosx-0)-sinx(sinx-0)+2(0-0)=0}$

$\mathsf{cos^2x-sin^2x=0}$

$\mathsf{cos\,2x=0}$

$\boxed{\mathsf{cos\theta=0\;\implies\;\theta=(2n+1)\dfrac{\pi}{2}}}$

$\implies\mathsf{2x=(2n+1)\dfrac{\pi}{2}\;\;\;n\;\in\;Z}$

$\implies\boxed{\mathsf{x=(2n+1)\dfrac{\pi}{4}\;\;\;n\;\in\;Z}}$

$\textbf{Find more:}$

Find the general solution of sin 3x = 0​

https://brainly.in/question/14908273