Let $$A$$ be the matrix $$\left[ {\matrix{ 3 & 1 \cr 1 & 2 \cr } } \right]$$. What is the maximum value of $${x^T}Ax$$ where the maximum is taken over all $$x$$ that are the unit eigenvectors of $$A$$?

The determination of the matrix given below is $$$\left[ {\matrix{ 0 & 1 & 0 & 2 \cr { - 1} & 1 & 1 & 3 \cr 0 & 0 & 0 & 1 \cr 1 & { - 2} & 0 & 1 \cr } } \right]$$$

The number of different $$n \times n$$ symmetric matrices with each elements being either $$0$$ or $$1$$ is

What values of x, y and z satisfy the following system of linear equations? $$$\left[ {\matrix{ 1 & 2 & 3 \cr 1 & 3 & 4 \cr 2 & 3 & 3 \cr } } \right]\,\,\left[ {\matrix{ x \cr y \cr z \cr } } \right]\,\, = \,\left[ {\matrix{ 6 \cr 8 \cr {12} \cr } } \right]$$$