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.

Find the scalar components of the vector $\stackrel{\rightarrow}{A B}$ with initial point A(2,1) and terminal point B (– 5, 7).

If $\stackrel{\rightarrow}{a}\$and $\stackrel{\rightarrow}{b}\$ are two unit vectors such that $\stackrel{\rightarrow}{a}\$ +$\stackrel{\rightarrow}{b}\$ is also a unit vector, then find the angle between $\stackrel{\rightarrow}{a}\$ and $\stackrel{\rightarrow}{b}\$

If f(x) = 27x³ and g(x) = $x^{1/3}$, then find gof(x).

If A is square matrix of order 2 and $|a d j A|=9,$ , find | A |.

Find the solution of the differential equation ${\frac{d y}{d x}}=x^{3}e^{-2y}$.

If matrix A = $\left(\begin{array}{l l }2 & -2 \\ -2 & 2\end{array}\right)$ and A² = pA, then write the value of p.