Question

Give an example of a skew symmetric matrix of order 3.

Find a unit vector parallel to the sum of vectors $\stackrel{\wedge}{i}+\stackrel{\wedge}{j} +\stackrel{\wedge}{k}$ and $2\stackrel{\wedge}{i}-3\stackrel{\wedge}{j} +5\stackrel{\wedge}{k}$

If m and n are the order and degree, respectively of the differential equation $\textstyle y\left({\frac{d y}{d x}}\right)^{3}+x^{3}\left({\frac{d^{2}y}{d x^{2}}}\right)^{2}-x y$= sin x, then write the value of m + n.

If matrix A = $\left(\begin{array}{l l }1 & -1 \\ -1 & 1\end{array}\right)$ and A² = kA, then write the value of k.

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

Write a unit vector in the direction of the sum of vectors ${\vec{a}}{=}2\,\vec{i}+2\,\vec{j}-5\,\vec{k}\ \mathrm{~and}\ \vec{b}=2\,\vec{i}+\vec{j}-{7}\vec{k}.$

If $(2x\ \ 4){\binom{x}{-8}}=0,$ find the positive value of x.