Question: 8. A linear transformation 7: V, -> 's maps the basis vectors as follows: T(i) = (1, 0, 1), TO) = (-1,0, 1). (a) Compute

8. A linear transformation 7: V, -> 's maps the basis vectors as follows: T(i) = (1, 0, 1), TO) = (-1,0, 1). (a) Compute 7(27 - 3j) and determine the nullity and rank of T. (b) Determine the matrix of T. (c) Find bases (e,, e,) for V, and (w,, wa, wa) for I's relative to which the matrix of Twill be in diagonal form

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