For the matrix $$P = \left[ {\matrix{ 3 & { - 2} & 2 \cr 0 & { - 2} & 1 \cr 0 & 0 & 1 \cr } } \right],$$ one of the eigen values is $$-2.$$ Which of the following is an eigen vector?

In the matrix equation $$PX=Q$$ which of the following is a necessary condition for the existence of atleast one solution for the unknown vector $$X.$$

for the scalar field $$u = {{{x^2}} \over 2} + {{{y^2}} \over 3},\,\,$$ the magnitude of the gradient at the point $$(1,3)$$ is

For the equation $$\,\,\mathop x\limits^{ \bullet \bullet } \left( t \right) + 3\mathop x\limits^ \bullet \left( t \right) + 2x\left( t \right) = 5,\,\,\,$$ the solution $$x(t)$$ approaches the following values as $$t \to \infty $$