Use Lagrange's method to find the maximum value of $\langle A\mathbf{x},\mathbf{x}\rangle$ subject to condition $\langle \mathbf{x},\mathbf{x}\rangle=1$ and $\langle \mathbf{u}_1,\mathbf{x}\rangle =0$ where $\mathbf{u}_1$ is a non zero vector in $N(s_1^2I_n-A^TA)$, $s_1$ is the largest singular value of A and $A=A^T \in \mathbb{R}^{n\times n}$.
Can anybody please explain me how to proceed with this question?