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Unformatted text preview: M340L Final Exam, May 13, 2010 1. (10 points) The matrix A = 1 1 3 1 7 7 1 2 5 3 20 16 2 4 10 7 45 36 is rowequivalent to 1 1 1 2 1 2 3 1 1 5 4 . a) Are the vectors 1 1 2 , 1 2 4 , and 3 5 10 linearly independent? b) Do the vectors 1 1 2 , 1 2 4 , 3 5 10 1 3 7 , 7 20 45 and 7 16 36 span R 3 ? c) Find bases for the column space of A , for the row space of A , and for the null space of A . 2 (15 points) Let B = 1 , 1 1 , 1 1 1 be a basis for R 3 , and let E be the standard basis. a. Compute the changeofbasis matrices P EB and P BE . b. If x = 3 2 5 , what is [ x ] B ? c. Let T : R 3 R 3 be a linear transformation given by the formula T ( x ) = 3 x 1 + 2 x 2 + x 3 2 x 1 x 3 x 2 . Find the standard matrix of....
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 Spring '08
 PAVLOVIC

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