•  Q1 Evaluate the determinants \begin{vmatrix} \mathbf{2} & \mathbf{4} \\ \mathbf{-5} & \mathbf{-1} \end{vmatrix} Q2 Evaluate the determinants (i) \begin{vmatrix} \mathbf{Cosθ} & \mathbf{−sin θ} \\ \mathbf{sin θ} & \mathbf{cos θ} \end{vmatrix}(ii) \begin{vmatrix} \mathbf{x^2 − x + 1} & \mathbf{x − 1} \\ \mathbf{x + 1} & \mathbf{x + 1} \end{vmatrix} Q3 If A=$$\begin{bmatrix}1 & 2\\4 & 2\end{bmatrix}$$, then show that |2A| = 4|A| Q4 If A=$$\begin{bmatrix}1 & 0 & 1\\0 & 1 & 2\\0 & 0 & 4\end{bmatrix}$$, then show that |3A| = 27|A|. Q5 Evaluate the determinants (i) $$\begin{vmatrix}3 & -1 & -2\\0 & 1 & 2\\0 & 0 & 4\end{vmatrix}$$ (iii) $$\begin{vmatrix}3 & -4 & 5\\1 & 1 & -2\\2 & 3 & 1\end{vmatrix}$$ (ii) $$\begin{vmatrix}0 & 1 & 2\\-1 & 0 & -3\\-2 & 3 & 0\end{vmatrix}$$(iv) $$\begin{vmatrix}2 & -1 & -2\\0 & 2 & -1\\3 & -5 & 0\end{vmatrix}$$ Q6 If A = $$\begin{bmatrix}1 & 1 & -2\\2 & 1 & -3\\5 & 4 & -9\end{bmatrix}$$, Find |A| Q7 Find values of x, if (i) $$\begin{vmatrix}2 & 4\\2 & 1\end{vmatrix}$$ = $$\begin{vmatrix}2x & 4\\6 & x\end{vmatrix}$$ (ii) $$\begin{vmatrix}2 & 3\\4 & 5\end{vmatrix}$$ = $$\begin{vmatrix}x & 3\\2x & 5\end{vmatrix}$$