Question

Write fog, if f : R → R and g : R → R are given by f(x) = |x| and g(x) = |5x - 2|.

If A is a square matrix of order 3 such that $|a d j\,A|$ = 225, find $|A^{\prime}|.$

If matrix A = $\left(\begin{array}{l l }3 & -3 \\ -3 & 3\end{array}\right)$ and A² = λA, then write the value of λ.

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

Write a unit vector in the direction of the sum of vectors ${\vec{a}}{=}2\,\vec{i}+2\,\vec{j}-5\,\vec{k}\ \mathrm{~and}\ \vec{b}=2\,\vec{i}+\vec{j}-{7}\vec{k}.$

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

Write the value of $\textstyle\int\!{\frac{1-\sin x}{\cos^{2}x}}\,d x\,.$