The equation $$\left[ {\matrix{ 2 & 1 & 1 \cr 1 & 1 & { - 1} \cr y & {{x^2}} & x \cr } } \right] = 0$$ represents a parabola passing through the points.

In matrix algebra $$AS=AT$$ ($$A,S,T,$$ are matrices of appropriate order) implies $$S=T$$ only if

The real symmetric matrix $$C$$ corresponding to the quadratic form $$Q = 4{x_1}{x_2} - 5{x_2}{x_2}$$ is

Obtain the eigen values and eigen vectors of $$A = \left[ {\matrix{ 8 & -4 \cr 2 & { 2 } \cr } } \right].$$