If the matrix A is such that $$$A = \left[ {\matrix{ 2 \cr { - 4} \cr 7 \cr } } \right]\,\,\left[ {\matrix{ 1 & 9 & 5 \cr } } \right]$$$ then the determinant of A is equal to _________.

Which one of the following statements is TRUE about every $$n\,\, \times \,n$$ matrix with only real eigen values?

If $${V_1}$$ and $${V_2}$$ are 4-dimensional subspaces of a 6-dimensional vector space V, then the smallest possible dimension of $${V_1}\, \cap \,\,{V_2}$$ is _________________.

The value of the dot product of the eigenvectors corresponding to any pair of different eigen values of a 4-by-4 symmetric positive definite matrix is ____________.