Question

If A = $\left(\begin{array}{l l }cosα & sinα \\ -sinα & cosα\end{array}\right)$ , find α satisfying $0\leq\alpha\leq{\frac{\pi}{4}}$ when $A+A^{T}=\sqrt{2}I$ where $A^{T}$ is transpose of A.

State the reason for the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} not to be transitive.

If $\left(\begin{array}{l l }x-y & 2y \\ 2y+z & x+y\end{array}\right)$ = $\left(\begin{array}{l l }1 & 4 \\ 9 & 5\end{array}\right)$

Find the differential equation representing the family of curves $V={\frac{A}{r}}+B,$ where A and B are arbitrary constants.

Find the sum of the vectors : $\stackrel{\rightarrow}{a}=\hat{i}-3\hat{k},$ ${\vec{b}}=2{\hat{j}}-{\hat{k}},$ $\stackrel{\rightarrow}{c}=2\hat{i}-3\hat{j}+2\hat{k}.$

If Δ = $\begin{vmatrix}5 & 3 & 8 \\ 2 & 0 & 1 \\ 1 & 2 & 3\end{vmatrix}$ , write the minor of the element $a_{23}.$

Write a unit vector in the direction of the sum of vectors : $\stackrel{\rightarrow}{a}\ = 2\stackrel{\wedge}{i}-\stackrel{\wedge}{j} +2\stackrel{\wedge}{k} and \stackrel{\rightarrow}{b}\ = \stackrel{\wedge}{i}+\stackrel{\wedge}{j} +3\stackrel{\wedge}{k}$