Problems on linear algebra-orthogonal basis

Question

Question:

Linear Algebra : Orthogonal Basis

Problem

A. Quote a theorem which guarantees that there exists an orthogonal basis for (with standard inner product) made up of eigenvectors of matrix

                               A =  [ 2     1       1 ]
                                      [ 1     2       1 ]
                                      [ 1     1       2 ]

B. Find such a basis β.

C. Represent the quadratic form Q (x,y,z) = 2 ( x2 + y2 +z2 +xy +xz + yz) by a symmetric matrix. Is Q positive definite?