Question: Please answer questions 3 and 4. FULL WORK SHOWN!!! I need everything step by step! Please please please answer in a legible handwriting! (I hate

Please answer questions 3 and 4. FULL WORK SHOWN!!!

I need everything step by step! Please please please answer in a legible handwriting! (I hate having to submit a question twice because it is impossible to read! And double check your answers, I have had a few wrong answers in linear algebra lately... Thank you so much

Question 4 (10 points). Let A be an m by n matrix. In a very brief para- graph, explain why n = NulA + rankA.Question 3 (10 points). Let V and W be two finite dimensional (real) vector spaces and T : V - W a linear tranformation from V to W. Let Im (T) = {T(v) E W | VEV}. Prove the following: (a) Im T is a subspace of W. (b) If T is one-to-one and onto (that is, if T is an isomorphism), then dim V = dim W

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