Question: Let B = {v1, v2, v3, v4} be a basis for a vector space L, and let T: V V be the linear operator

Let B = {v1, v2, v3, v4} be a basis for a vector space L, and let T: V → V be the linear operator for which
T(v1) = v1 + v2 + v3 + 3v4
T(v2) = v1 - v2 + 2v3 + 2v4
T(v3) = 2v1 - 4v2 + 5v3 + 3v4
T(v4) = -2v1 + 6v2 - 6v3 - 2v4
(a) Find the rank and nullity of T.
(b) Determine whether T is one-to-one.

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