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Unformatted text preview: . (a) Find a basis for Col A . (b) Find a basis for Nul A . (c) Find a basis for the row space of A . (d) What is the dimension of Col A ? (e) What is the dimension of Nul A ? (f) What is the rank of A ? 5. (6 points each) (a) Use coordinate vectors to show that B = { 1 , t1 , ( t1) 2 } is a basis for the vector space of polynomials of degree at most 2. (b) Continuing from (a), nd q ( t ) if [ q ] B = 1 3 2 . (c) Continuing from (a), nd [ r ] B if r ( t ) = 1 + 3 t + 2 t 2 . 6. (8 points) Let D = { d 1 , d 2 , d 3 } and G = { g 1 , g 2 , g 3 } be bases for a vector space V , and suppose g 1 = 3 d 12 d 2 + d 3 , g 2 = d 1 + d 2 + 2 d 3 , and g 3 =d 1 + 2 d 2 + d 3 . (a) Find the changeofcoordinates matrix from G to D . (b) Find [ x ] D if x = 2 g 13 g 2 + g 3 . 7....
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 Fall '08
 PAVLOVIC

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