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

$$A$$ is a $$3 \times 4$$ matrix and $$AX=B$$ is an inconsistent system of equations. The highest possible rank of $$A$$ is

For what value of $$x$$ will the matrix given below become singular? $$\left[ {\matrix{ 8 & x & 0 \cr 4 & 0 & 2 \cr {12} & 6 & 0 \cr } } \right]$$

The sum of the eigen values of the matrix $$\left[ {\matrix{ 1 & 1 & 3 \cr 1 & 5 & 1 \cr 3 & 1 & 1 \cr } } \right]$$ is