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Unformatted text preview: Print Name: Student Number: Section Time: Math 20F. Final Exam March 20, 2006 Read each question carefully, and answer each question completely. Show all of your work. No credit will be given for unsupported answers. Write your solutions clearly and legibly. No credit will be given for illegible solutions. 1. Consider the matrix A = 1- 1 5 1- 2 1 3- 3 . (a) (5 Pts.) Find a basis for the subspace of all vectors b such that the linear system A x = b has solutions. Show your work. (b) (5 Pts.) Find a basis for the null space of A . Show your work. (c) (5 Pts.) Find a solution to the linear system A x = b with b = 1 1 5 . Is this solution unique? If yes, say why. If no, find a second solution x with the same b . # Score 1 2 3 4 5 6 7 8 2. Let u = 1 1 , v = 1- 1 , and T : IR 2 IR 2 be a linear transformation given by T ( u ) = 1 3 , T ( v ) = 3 1 ....
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- Winter '03