Question

Write the solution of the differential equation ${\frac{d y}{d x}}=2^{-y}.$

Find the magnitude of each of the vectors $\stackrel{\rightarrow}{a}$ and $\stackrel{\rightarrow}{b}$,having the same magnitude such that the angle between them is 60° and their scalar product is ${\frac{9}{2}}.$

Evaluate : $\textstyle\int$ cos⁻¹(sin x) dx.

Write a vector in the direction of the vector $\displaystyle{\hat{\iota}}-2\,{\hat{\iota}}+2\,{\hat{\iota}}$ that has magnitude 9 units.

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.

The two vectors $:{\hat{j}}+{\hat{k}}$ and $3\stackrel{\wedge}{i}-\stackrel{\wedge}{j} +4\stackrel{\wedge}{k}$ represent the two sides AB and AC, respectively of $\Delta A B C.$ Find the length of the median through A.

Let A = $A\ =\ {\left(\begin{array}{l l}{2}&{-1}\\ {3}&{4}\end{array}\right)}$ , B = $A\ =\ {\left(\begin{array}{l l}{5}&{2}\\ {7}&{4}\end{array}\right)}$ , C = $A\ =\ {\left(\begin{array}{l l}{2}&{5}\\ {3}&{8}\end{array}\right)}$ , find a matrix D such that CD - AB = 0.