Given that A is a n x n symmetric matrix and $\displaystyle \lambda_{1} \geq \lambda_{2} \geq .... \geq \lambda_{n} $ , where $\displaystyle \lambda_{i} $ are eigenvalues of A.

Show that:

$\displaystyle

\lambda_{1}\|x\|^{2} \geq x^{T}Ax \geq \lambda_{n}\|x\|^{2}

$

Having trouble proving the above ! Any help would be much appreciated.