Past exam of the numerical linear algebra and continuous optimisation course of the University of Oxford / 2010 / A / 3 / b / Solution

A real symmetric matrix is positive-definite when $x^{T}Ax>0$ for every nonzero real vector $x$. The preceding matrix 2-norm bound givesThus $A$ is a symmetric positive-definite matrix, independently of the detailed positions of the nonzero entries of $t$.