The system of equations, given below, has $$$x+2y+4z=2$$$ $$$4x+3y+z=5$$$ $$$3x+2y+3z=1$$$

For the matrix $$A = \left[ {\matrix{ 5 & 3 \cr 1 & 3 \cr } } \right],$$ ONE of the normalized eigen vectors is given as

The eigen values of the following matrix $$\left[ {\matrix{ {10} & { - 4} \cr {18} & { - 12} \cr } } \right]$$ are

The value of $$q$$ for which the following set of linear equations $$2x+3y=0, 6x+qy=0$$ can have non-trivial solution is