Question

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

Is A is square matrix of order 3 and |2A| = k|A|, then find the value of k.

If f : R→ R defined by f(x) = $\textstyle{\frac{3x+5}{2}}$ is an invertible function, then find $f^{-1}(x).$

If A = $\left(\begin{array}{l l}{{0}}&{{3}}\\ {{2}}&{{-5}}\end{array}\right)$ and $K A\ =\ {\left(\begin{array}{l l}{0}&{4a}\\ {-8}&{5b}\end{array}\right)}$ find the values of k and a.

For what values of $\stackrel{\rightarrow}{a}\$, the vectors $2\stackrel{\wedge}{i}-3\stackrel{\wedge}{j} +4\stackrel{\wedge}{k}$ and $a\,{\hat{\boldsymbol{i}}}+6\,{\hat{\boldsymbol{j}}}-8\,{\hat{\boldsymbol{k}}}$ are collinear?

Find ‘λ’ when the projection of $\stackrel{\rightarrow}{a}\$ = $λ\stackrel{\wedge}{i}+\stackrel{\wedge}{j} +4\stackrel{\wedge}{k}$ on $\stackrel{\rightarrow}{b}\$ = $2\stackrel{\wedge}{i}+6\stackrel{\wedge}{j} +3\stackrel{\wedge}{k}$ is 4 units.

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