Question

Write the inverse of the matrix $\left(\begin{array}{l l }cosθ & -sinθ \\ sinθ & cosθ\end{array}\right)$ .

If $\left(\begin{array}{l l }2x & 3\end{array}\right)$ $\left(\begin{array}{l l }1 & 2 \\ -3 & 0\end{array}\right)$ $\left(\begin{array}{l }x \\ 3\end{array}\right)$ = 0,

If ${\left[\begin{array}{l l}{a+4}&{3b}\\ {8}&{-6}\end{array}\right]}={\left[\begin{array}{l l}{2a+2}&{b+2}\\ {8}&{a-8b}\end{array}\right]},$ write the value of a – 2b.

If $\begin{vmatrix} \sin\alpha & \cos\beta \\ \cos\alpha & \sin\beta \end{vmatrix} =-\ {\begin{array}{l}{1}\\ {2}\end{array}}\$ where α and β are acute angles, then write the value of α + β .

Evaluate: $\textstyle\int\cot{x}(cosec x-1)e^{x}d x$ .

Evaluate $\textstyle\int$ sec² (7 – 4x) dx.

If matrix A = $\left(\begin{array}{l l }1 & -1 \\ -1 & 1\end{array}\right)$ and A² = kA, then write the value of k.