The matrix $$\left[ {\matrix{ 1 & 2 & 4 \cr 3 & 0 & 6 \cr 1 & 1 & P \cr } } \right]$$ has one eigen value to $$3.$$ The sum of the other two eigen values is

For what values of 'a' if any will the following system of equations in $$x, y$$ and $$z$$ have a solution? $$$2x+3y=4,$$$ $$$x+y+z=4,$$$ $$$x+2y-z=a$$$

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

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