1.

Find the inverse of each of the matrices,if it exists \(\begin{bmatrix} 2 & 1 \\ 7 & 4  \end{bmatrix}\)

2.

Find the inverse of each of the matrices,if it exists. \(\begin{bmatrix} 2 &  3\\ 5 & 7 \end{bmatrix}\)

3.

If A'= \(\begin{bmatrix} 3 & 4 \\ -1 & 2 \\ 0 &1 \end{bmatrix}\)\(\begin{bmatrix}  -1 & 2 & 1 \\ 1 &2 & 3\end{bmatrix}\) , then verify that 
(i) \((A+B)'=A'+B' \)
(ii) \((A-B)'=A'-B'\)

4.

If (i) A=\(\begin{bmatrix} \cos\alpha & \sin\alpha\\ -\sin\alpha & \cos\alpha \end{bmatrix}\),then verify that A'A=I
(ii) A= \(\begin{bmatrix} \sin\alpha & \cos\alpha\\ -\cos \alpha & \sin\alpha \end{bmatrix}\),then verify that A'A=I

5.

A circular disc is rotating about its own axis. An external opposing torque 0.02 Nm is applied on the disc by which it comes rest in 5 seconds. The initial angular momentum of disc is

• $0.1\,kgm^2s^{-1}$
• $0.04\,kgm^2s^{-1}$
• $0.025\,kgm^2s^{-1}$
• $0.01\,kgm^2s^{-1}$

6.

Evaluate \(\begin{vmatrix} cos\alpha cos\beta &cos\alpha sin\beta  &-sin\alpha \\   -sin\beta&cos\beta  &0 \\   sin\alpha cos\beta&sin\alpha\sin\beta  &cos\alpha  \end{vmatrix}\)