Let A be an invertible n X 11 matrix. There is an inner product on R" which we will denote throughout this question by (35,35) = (A35) - (A37)- (a) Use 3' to denote the orthogonal complement of a subspace S under this inner product; we'll reserve $1 for the orthogonal complement under clot product. Prove or disprove: S" = Si. (b) State a modified version of the fundamental theorem of linear algebra for an n X 71 matrix B which replaces J. everywhere with o. (e) Let (, ) denote a third inner product on IR"; let {E51 , . .. , 5"} be an orthonormal basis for (, ). Prove or disprove: if A is the invertible matrix with columns given by a] , . .. , a", then (35, B = (if, 33) for all SE, 35 E IR"