List of top Mathematics Questions on Matrix Algebra asked in NIMCET

The number of values of \(\theta\) in \([0,2\pi]\) for which the following homogeneous system has a non-trivial solution is: \[ x+(\sin\theta)y+(\cos\theta)z=0 \] \[ x+(\cos\theta)y+(\sin\theta)z=0 \] \[ x-(\sin\theta)y-(\cos\theta)z=0 \]

Find the value of determinant at \(x=2026\): \[ \begin{vmatrix} x & x+1 & x+3\\ x+1 & x+3 & x+6\\ x+3 & x+6 & x+10 \end{vmatrix} \]