09-27-10 - R 3 Why or why not 4 Suppose T has the property...

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Math 54 Discussion Section Problems Mike Hartglass September 27, 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. Find the β -coordinate vector for p ( t ) = 3 - 8 t + 4 t 2 where β = { 1 + t 2 ,t + t 2 , 1 + 2 t + t 2 } 2. For each part below, determine if T is a linear transformation. (a) T : P 3 R given by T ( p ) = p (1) (b) T : R 3 R 3 given by T x y z = x + 1 y z 3. Suppose T has the property that T 2 1 0 = 0 1 0 , T - 1 1 0 = 1 0 0 T 1 2 1 = 0 0 1 . Can T be extended to a linear transformation defined on all of
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Unformatted text preview: R 3 ? Why or why not. 4. Suppose T has the property that T 2 1 = 1 , T -1 1 = 1 T 1 2 = 1 . Can T be extended to a linear transformation defined on all of R 3 ? Why or why not. 5. Let T : R 4 → R 6 be a linear transformation. Find all possible values for the dimensions of the null space and range of T . 6. Let A be some fixed 3 × 4 matrix. Prove that the set { B ∈ M 4 × 2 : AB = 0 } is a subspace of M 4 × 2 ....
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