Gif a is a real n×n matrix, then we have seen that < v, w > a: = v t ∗a∗ w defines a bilinear pairing on r n which is symmetric iff a is a symmetric matrix. if a is symmetric, we call a positive definite iff < v, v > a > 0 for all 0 6= v ∈ r n (in other words, < −,− > a is an inner product on r n). a) [1 pt] suppose b is the matrix given by b = 1 1 1 2 and x = [x1 x2] t ∈ r 2 . find an expression for x t ∗ b ∗ x in terms of x1 and x2. b) [1 pt] using your work in part a), show that the matrix b above is positive definite.