The value of $$'x'$$ for which all the eigenvalues of the matrix given below are real is $$\left[ {\matrix{ {10} & {5 + j} & 4 \cr x & {20} & 2 \cr 4 & 2 & { - 10} \cr } } \right]$$

Which one of the following statements is NOT true for a square matrix $$A$$?

The maximum value of the determinant among all $$2 \times 2$$ real symmetric matrices with trace $$14$$ is ______.

The system of linear equations $$\left( {\matrix{ 2 & 1 & 3 \cr 3 & 0 & 1 \cr 1 & 2 & 5 \cr } } \right)\left( {\matrix{ a \cr b \cr c \cr } } \right) = \left( {\matrix{ 5 \cr { - 4} \cr {14} \cr } } \right)$$ has