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LINALG040Dec2007

# LINALG040Dec2007 - Thursday Page 1 Linear Algebra 040a...

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Thursday, December 13, 2007 Page 1 Linear Algebra 040a Final Examination 1. 8 marks Let T : R 3 R 2 be the linear transformation with standard matrix M = ± 1 1 1 1 2 3 ! . (a) Calculate T (2 e 1 + e 2 - e 3 ). (b) The set B = ² v 1 = ± 1 1 ! , v 2 = ± 1 - 1 is a basis of R 2 . Order this basis as v 1 , v 2 . Find the coordinate vector of T ( e 2 ) with respect to this ordered basis.

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Linear Algebra 040a Final Examination Thursday, December 13, 2007 Page 2 2. 7 marks Find the rank of the matrix A = 1 1 2 0 0 0 1 1 0 0 1 2 1 1 3 1 2 2 4 0 .
Thursday, December 13, 2007 Page 3 Linear Algebra 040a Final Examination 3. 8 marks Let W = span 1 0 0 0 1 , 2 1 0 0 0 , 1 3 - 1 1 1 . Find a basis for W ,

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Linear Algebra 040a Final Examination Thursday, December 13, 2007 Page 4 4. 7 marks The matrix A is a 605 × 522 matrix with nullity of A T = 210. Find the nullity of A .
Thursday, December 13, 2007 Page 5 Linear Algebra 040a Final Examination 5. 7 marks Let A = 2 0 - 2 4 0 - 4 0 0 0 0 0 1 Find a 4 × 2 matrix C with full column rank and a 2 × 3 matrix R with full row rank so that A = CR .

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LINALG040Dec2007 - Thursday Page 1 Linear Algebra 040a...

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