Question

If matrix A = $[a_{i j}]_{2\times2}$, where $a_{i j}$ = $\left\{\begin{array}{l}{{2,\ i\neq j}}\\ {{0,\ i=j^{\prime}}}\end{array}\right.$ , Write the matrix A.

If $\stackrel{\rightarrow}{a}\$ and $\stackrel{\rightarrow}{b}\$ are perpendicular vectors, $|\stackrel{\rightarrow}{a}\$ + $\stackrel{\rightarrow}{b}|\$ = 13 and $|\stackrel{\rightarrow}{a}|\$ =5,find the value of $|\stackrel{\rightarrow}{b}|\$.

Evaluate: $\textstyle\int(1-x){\sqrt{x}}\,d x~.$

If A is a 3 × 3 matrix, $|A|\neq0$ and $|3A|\,=\,k|A|,$ then write the value of k.

Find : $\int{\frac{\sin^{2}x-\cos^{2}x}{\sin x\cos x}}\,d x$

If the following function f(x) is continuous at x = 0, then write the value of k.

If A is an invertible square matrix of order 3 and |A| = 5, then find the value of |adj A|.