Let $$A$$ be $$3 \times 3$$ matrix with rank $$2.$$ Then $$AX=O$$ has

The value of the integral $$\int\limits_{ - 1}^1 {{1 \over {{x^2}}}dx} \,\,\,$$ is

$$f = {a_0}\,{x^n} + {a_1}\,{x^{n - 1}}\,y + - - + \,{a_{n - 1}}\,x\,{y^{n - 1}} + {a_n}\,{y^n}$$
where $$\,\,{a_i}\,\,$$ ($$i=0$$ to $$n$$) are constants then $$x{{\partial f} \over {\partial x}} + y{{\partial f} \over {\partial y}}\,\,\,$$ is

If a vector $$\overrightarrow R \left( t \right)$$ has a constant magnitude then