100212 - Answers to your questions 02/12/10: Administrative...

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Answers to your questions 02/12/10: Administrative questions 1. If we don’t have enough questions for a certain day, will we not receive full extra credit points? The credits you get depend on the total number of questions you asked. So even if you are absent for one day, it doesn’t matter. 2. I think this idea of writing down our questions is a great idea. Thanks for the feedback. I appreciate it. 3. Do you recommend any supplementary books/texts for extra practice? I think it will be very helpful if you have time to go over other exercises in our textbook. Questions on general topics 4. What is the difference between S1=a1x1+a2x2+ … + anxn and span(S1)? Can we write span(a1x1+a2x2+ … + anxn)? In S1=…, S1 is a vector that is expressed as linear combination of x’s. In span(S1), if S1 is a set, it means linear combination of vectors in S1. If S1 is a vector, span(S1) means multiples of S1. Given specific values of a’s, span(a1x1+a2x2+ … + anxn) means multiple of the vector a1x1+a2x2+ … + anxn. 5. Let u,v,w be distinct vectors of a vector space V. Show that if {u,v,w} is a basis for V, then {u+v+w, v+w, w} is also a basis for V. Why do we need span{u+v+w, v+w, w}=V? When do we need to use span? We don’t need span in this problem since we already know that the dimension is 3. If we don’t
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100212 - Answers to your questions 02/12/10: Administrative...

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