09-10-10 - (a) T x y = y x (b) T ( x ) =-x (c) T rotates...

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Math 54 Discussion Section Problems Mike Hartglass September 10, 2010 You should work on the following problems in groups of 3 or 4. Try to get through as many as you can, but you aren’t expected to finish everything. In fact, the answers are largely unimportant; making sure everyone in your group knows how to solve all the problems is what really matters. 1. Let A = 1 3 - 5 0 4 - 8 - 3 - 7 9 , B = 1 3 0 - 2 1 4 and C = ± 1 - 1 2 ² . Find the following expressions or explain why they do not exist. (a) AB (b) BA (c) AC (d) CA (e) A - 1 (f) B - 1 2. Let T be a linear transformation whose matrix is given by A = 1 3 - 5 1 4 - 8 - 3 - 7 9 . (a) What are the domain and co-domain of T ? (b) Is 4 7 - 6 in the range of T ? (c) Find the range of T . (d) Are the columns of A linearly independent? 3. Find the matrix that corresponds to each of the following linear transformations:
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Unformatted text preview: (a) T x y = y x (b) T ( x ) =-x (c) T rotates vectors clockwise by 90 4. What are the domain and codomain of T if the matrix for T is 4x3? 2x4? 5. Let A = 1-3 2-3 9-6-2 6-4 (a) Find all solutions to A x = 0 (b) Does this set of solutions form a subspace? (c) Write your answer to part (a) as the span of some set of vectors. (d) Suppose someone gives you a vector b and tells you that A 1-1 = b . Find the general solution to A x = b . Is this a subspace of R 3 ? Can it be written as the span of some set of vectors? Why or why not?...
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