10_28_challenge_questions - F(The small F is transformed to...

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Challenge Questions: 10-28-2011 MA2940: Linear Algebra for Engineers 1) Let U and V we subdimensional subspaces of R 5 . Show that W = U V is also a subspace of R 5 . What are all possible dimensions of W ? 2) A is a linear transformation from R 3 to R 2 , and B is a linear transformation from R 2 to R 3 . Show the the linear transformation AB cannot be invertible. What about BA ? Why? 3) Find a linear map of the plane A : R 2 R 2 that does the following transformation to the letter
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Unformatted text preview: F. (The small F is transformed to the large one). Is your map unique? Find an inverse map that takes the big F back to the small one. 4) P is a plane in R 3 defined by x-2 y-2 z = 0. Recall, the orthogonal complement P ⊥ was all vectors ± v : v T p = 0 , for every p ∈ P ² . What if we replace v T p = 0 with v T p = 1? Describe what changes. TA: Kyle Wilson...
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