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Unformatted text preview: Answers to your questions 02/10/10: Administrative questions 1. For the quiz tomorrow, since no hw was given this week, what type of problems should we expect? For example, problem 2,3,4 in section 2.2 and the examples in class. Questions on general topics 2. Subspaces are vector spaces on their own, right? Yes. 3. What does the span of the subset do to the subspaces W in V when it says: S span W. It means, each vector in W is a linear combination of S. 4. What is the difference from a subset S and subspace W in V? A subspace is closed under addition and scalar multiplication, and has a zero, whereas a subset is not necessarily. 5. If v is a vector in V, and W, U are subspace of V, does it mean v is in W and v is in U? No. v can be outside of W or U, or inside W or U. Questions for todays lecture 6. For the last example in 2.2, you said that (3,1,1) was a standard basis, but I thought {(1,0,0),(0,1,0),(0,0,1)} was the standard basis. I said (3,1,1) was the coordinate vector in terms of the standard basis. And you are right about the standard basis. 7. For matrix representation problems, if given g and G , if it does not state they are bases, do we assume they are basis or do we have to show they are bases first? If they are not the bases, you cannot find the matrix representation based on them. Hence they must be bases....
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