Worksheet5 - b 4 = 2 1 1 6 5. Consider the set W of vectors...

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Worksheet 5 February 9th, 2009 1. Let A be an m × n matrix. Show that Nul A is a subspace of R n 2. Below a matrix A is given with an echelon form. Find a basis for Col A and a basis for Nul A . - 3 9 - 2 - 7 2 - 6 4 8 3 - 9 - 2 2 1 - 3 6 9 0 0 4 5 0 0 0 0 3. Let B = { b 1 , b 2 } be a new basis of R 2 , where b 1 = ± 1 1 ² and b 2 = ± 1 - 1 ² . Find the B coordinate vectors of ± 3 5 ² and ± x 1 x 2 ² 4. Find a basis for the subspace of R 4 spanned by the vectors: b 1 = 1 1 2 4 , b 2 = 2 - 1 - 5 2 b 3 = 1 - 1 - 4 0
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Unformatted text preview: b 4 = 2 1 1 6 5. Consider the set W of vectors of the form x y-x z . Is W a subspace of R 4 . If so prove it, if not explain why. 6. Let T : R 3 R 3 be a linear transformation such that T ( x,y,z ) = (7 x,x + z, 3 x-z ). Find the rank of T and the dimension of Nul ( T ). 1...
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