5. Consider the matrix of the linear transformation T given by rotation by the angle counterclockwise....

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5. Consider the matrix of the linear transformation T given by rotation by the angle counterclockwise. What is the matrix A and its inverse? Prove that A is orthogonal. (5 marks) 6. Determine the dimension of the subspace VC R generated by the set of 4-tuples {(1, 1, 1, 1), (1, 1, 1, 1), (1, 1, 1, 3), (1, 1, 1, 1)} Present one possible basis for V. 5. Consider the matrix of the linear transformation T given by rotation by the angle counterclockwise. What is the matrix A and its inverse? Prove that A is orthogonal. (5 marks) 6. Determine the dimension of the subspace VC R generated by the set of 4-tuples {(1, 1, 1, 1), (1, 1, 1, 1), (1, 1, 1, 3), (1, 1, 1, 1)} Present one possible basis for V.