6. Prove the following statements (a) Let V and W be finite-dimensional F-vector spaces, and let TV- W be a linear transformation. Then 3 linear transformation S: W → V such that S. T = Iv iff T is onto (b) Let A & Mmxn (F). Then 3 a matrix B € Mnxm (F) 5. t. BA = In iff rank (A) = h

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