For matrix $A=\left[\begin{array}{ccc}2& -1& 0\\ -1& 2& -1\\ 0& -1& 2\end{array}\right]$

a$)$ find the function $x^{T}Ax.$

b$)$ find the pivots of A and show they are all positive.

c$)$ find the eigenvalues of A and show they are all positive.

d$)$ Show $A$ is positive definite.