The number of linearly independent eigen vectors of $$\left[ {\matrix{ 2 & 1 \cr 0 & 2 \cr } } \right]$$ is

If a square matrix $$A$$ is real and symmetric then the eigen values

The partial differential equation $$\,\,{{{\partial ^2}\phi } \over {\partial {x^2}}} + {{{\partial ^2}\phi } \over {\partial {y^2}}} + {{\partial \phi } \over {\partial x}} + {{\partial \phi } \over {\partial y}} = 0\,\,\,\,$$ has

If $$\phi (x,y)$$ and $$\psi (x,y)$$ are function with continuous 2^nd derivatives then $$\phi (x,y)\, + \,i\psi (x,y)$$ can be expressed as an analytic function of x +iy ($$i = \sqrt { - 1} $$) when