Question: (i) [3 marks] Use lGramSchmidt process to convert the columns of A to an orthonormal basis T for RE. Show your working and give the

(i) [3 marks] Use lGramSchmidt process to convert the columns of A to an orthonormal basis T for RE. Show your working and give the exact values for the entries of the basis. Do not use MATLAB. (ii) [2 marks] Find the coordinate vectors of the columns of A with respect to the basis T. Write them as column vectors. (iii) [3 marks] Use (i) and (ii) above to express the matrix as A = QU, Where Q is an orthogonal matrix and U is an upper triangular matrix. Briey explain how you obtain the answer. (13) Prove the following statements. (i) [3 marks] The eigenvalues of an orthogonal matrix are :|:1. (ii) [3 marks} Suppose A is an diagonalisable orthogonal matrix. then A2 =

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