(1b) Consider the matrix 1 1 11 A-0 1 1 0 0 1 as an operator...

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(1b) Consider the matrix 1 1 11 A-0 1 1 0 0 1 as an operator that maps 3 by 1 column vectors, x, into 3 by 1 column vectors, y, so that Ax = y. [1] What is the matrix representation of this operator in the basis set 0 0. (3) What are the eigenvalues of this operator in this new basis set? (1c) Given a set of m by 1 column vectors x1, x2,...,xm that are linearly dependent show that the Gram matrix, G, defined by [(x,,x) (x1,x2) (x2, x) (x2, x2) G = {(x, x) (x,x) (x, x)] (x2, xm) (*,*)] (1b) Consider the matrix 1 1 11 A-0 1 1 0 0 1 as an operator that maps 3 by 1 column vectors, x, into 3 by 1 column vectors, y, so that Ax = y. [1] What is the matrix representation of this operator in the basis set 0 0. (3) What are the eigenvalues of this operator in this new basis set? (1c) Given a set of m by 1 column vectors x1, x2,...,xm that are linearly dependent show that the Gram matrix, G, defined by [(x,,x) (x1,x2) (x2, x) (x2, x2) G = {(x, x) (x,x) (x, x)] (x2, xm) (*,*)]