Exercise

A bilinear pairing on R2 is given on pairs of basis vectors by = 10, ==7, =5 a) Verify that defines an inner product on R?. b) Find the matrix A representing this inner product in the standard basis (as defined in the textbook). c) Compute where v = 3 d) For v as above, find a non-zero vector w satisfying =0. e) Give a basis for R that is orthogonal with respect to this inner product