Question

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

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.

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

Write the degree of the differential equation $\left({\frac{d^{2}s}{d t^{2}}}\right)^{2}+\left({\frac{d s}{d t}}\right)^{3}+4=0.$

If f is an invertible function, defined as f(x) = $\frac{3x-4}{5}$, then write $f^{-1}(x).$

If the determinant of matrix A of order 3 × 3 is of value 4, write the value of |3A|.

Find a vector in the direction of vector $2\stackrel{\wedge}{i}-3\stackrel{\wedge}{j} +6\stackrel{\wedge}{k}$which has magnitude 21 units.