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5. Prove or disprove the following statements. (a) Let L : V → W be a...

5. Prove or disprove the following statements.

(a) Let L : V → W be a linear mapping. If {L(~v1), . . . , L( ~vn)} is a basis for W, then {~v1, . . . , ~vn} is a basis for V.

(b) If V and W are both n-dimensional vector spaces and L : V → W is a linear mapping, then nullity(L) = 0.

(c) If V is an n-dimensional vector space and L : V → V is a linear operator such that ker(L) 6= {~0}, then {L(~v1), . . . , L( ~vn)} is linearly dependent.

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