Question

If A is a square matrix such that A² = A, then write the value of 7A – (I + A)³, where I is an identity matrix.

Write the projection of the vector $\stackrel{\wedge}{i}+\stackrel{\wedge}{j} +\stackrel{\wedge}{k}$ along the vector $\stackrel{\rightarrow}{j}\$.

If A = $\left(\begin{array}{l l }x & x-y \\ 2x+y & 7\end{array}\right)$ = $\left(\begin{array}{l l }3 & 1 \\ 8 & 7\end{array}\right)$ , then find the value of y.

If A is a 3 × 3 matrix, whose elements are given by $a_{i j}={\frac{1}{3}}|-3i+j\,|$ , then write the value of $a_{23}$.

If f : R → R is defined by f(x) = $(3-x^{3})^{1/3},$ then find fof(x).

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

If $\left(\begin{array}{l l l }1 & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & 1\end{array}\right)$ $\left(\begin{array}{l }x \\ -1 \\ z\end{array}\right)$ = $\left(\begin{array}{l }1 \\ 2 \\ 1\end{array}\right)$ , find x + y + z.