Exercise

If A is a real n x n matrix, then we have seen that A:=v A*w defines a bilinear pairing on R" which is symmetric iff A is a symmetric matrix. If A is symmetric, we call A positive definite iff A > 0 for all 0 # v ER" (in other words, <_>A is an inner product on R" ). a) Suppose B is the matrix given by B = 2 and x = [x1 x2]"ER'. Find an expression for x * B * x in terms of r, and r2. b) Using your work in part a), show that the matrix B above is positive definite