5. We say that the symmetric 2x2 matrix A=\left[\begin{array}{cc}

a_{11} & b \\

b & a_{22}

\end{array}\right], \quad a_{11}, b, a_{22} \in \mathbb{R} is strictly positive definite if \langle A h, h\rangle=a_{11} h_{1}^{2}+2 b h_{1} h_{2}+a_{22} h_{2}^{2}>0 \quad \forall h=\left[\begin{array}{l}

h_{1} \\

h_{2}

\end{array}\right] \in \mathbb{R}^{2} \backslash\{0\} (a) [8 pts] Show that the function h ↔ ||h||A=√(Ah, h) defines a norm on R². (b) [12 pts] Let F : R² → R be a function of class C². Suppose that the point x = (X1, X₂) €R2 is such that