Question

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

If A is a square matrix and | A | = 2, then write the value of | AA’ |, where A’ is the transpose of matrix A.

Write the value of $\begin{vmatrix}2 & 7 & 65 \\ 3 & 8 & 75 \\ 5 & 9 & 86\end{vmatrix}$

If $\stackrel{\rightarrow}{a}\$ and $\stackrel{\rightarrow}{b}\$ are unit vectors, then what is the angle between $\stackrel{\rightarrow}{a}\$ and $\stackrel{\rightarrow}{b}\$, so that ${\sqrt{2}}$ $\stackrel{\rightarrow}{a}\$ -$\stackrel{\rightarrow}{b}\$ is a unit vector ?

Write the value of $\textstyle\int\!{\frac{2-3\sin x}{\cos^{2}x}}\,d x$.

If A = $\left(\begin{array}{l l }3 & 4 \\ 2 & 3\end{array}\right)$then find A + A’., where A’ is transpose of A.

If A = $\left(\begin{array}{l l }3 & 10 \\ 2 & 7\end{array}\right)$ , then write A⁻¹.