List of top Engineering Mathematics Questions on Matrix

The system of equations \( \begin{bmatrix} -2 & 1 & 1 \\ 1 & -2 & 1 \\ 1 & 1 & -2 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} a \\ b \\ c \end{bmatrix} \) has
If \( \begin{bmatrix} \frac{1}{\sqrt{3}} & \frac{1+i}{\sqrt{3}} \\ \frac{1-i}{\sqrt{3}} & \frac{K}{\sqrt{3}} \end{bmatrix} \) is a unitary matrix, then the sum of all possible values of K is
If \( A \) is an orthogonal matrix, then \( A^{-1} \) is
Consider two matrices \[ P = \begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix}, Q = \begin{bmatrix} 5 & 4 \\ 0 & 2 \end{bmatrix}. \] If \(R = (PQ)^T\), then \(\det R\) is ............ (in integer).

The 2×2 matrices P and Q satisfy the following relations: 

The matrix Q is equal to _______.