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Unformatted text preview: Answers to your questions 02/19/10: Administrative questions 1. Are there going to be multiple trick questions on future worksheets? It depends on how you define “trick questions”. 2. It is very helpful when you review material from previous lectures at the beginning of the class. Thank you for the feedback. I appreciate it. 3. For our final exam, what sections/chapters are we covering up to? It is comprehensive. 1.1-4.4 Questions on general topics 4. What exactly is L(V,W)? Can you give examples? It is a very abstract concept. I cannot give explicit examples. You can think of a specific V and a specific W. For example, V=P2(R), W=R. Then L(V,W) in this case is the set of all linear transformations that maps a polynomial a+bx+cx^2 to a real number. It contains the transformations that maps a+bx+cx^2 to zero, to a, to b, to c, etc. (any linear transformations that you can think of) 5. What does linear transf. bB matrices mean? It means you can treat each linear transformation as a matrix, and each matrix as a linear transformation. There is a 1 to 1 correspondence between them. 6. What do you mean when you say “nice properties”? Like associative law, distributive law, the laws you already know. Questions for today’s lecture 7. What does it mean for T to be invertible? If T is a linear transformation from V to W, what does T^-1 do? T^-1 maps W to V. For example, T maps a to b, then T^-1 maps b to a....
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