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Winter 2006 - Nagy's Class - Exam 1 (Version B)

# Winter 2006 - Nagy's Class - Exam 1 (Version B) - Print...

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Print Name: Student Number: Section Time: Math 20F. Midterm Exam 1 February 8, 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. (10 points) Consider the matrix A and the vector b given by A = 1 - 2 - 1 - 6 2 3 - 2 1 1 , b = 2 3 4 . (a) Find the inverse of A . Justify your answer. (b) Find the solution of the non-homogeneous system A x = b . Justify your answer. (a) 1 - 2 - 1 | 1 0 0 - 6 2 3 | 0 1 0 - 2 1 1 | 0 0 1 1 - 2 - 1 | 1 0 0 0 - 10 - 3 | 6 1 0 0 - 3 - 1 | 2 0 1 1 - 2 - 1 | 1 0 0 0 1 3 / 10 | - 3 / 5 - 1 / 10 0 0 - 3 - 1 | 2 0 1 1 0 - 2 / 5 | - 1 / 5 - 1 / 5 0 0 1 3 / 10 | - 3 / 5 - 1 / 10 0 0 0 - 1 / 10 | 1 / 5 - 3 / 10 1 1 0 0 | - 1 1 - 4 0 1 0 | 0 - 1 3 0 0 1 | - 2 3 - 10 , A - 1 = - 1 1 - 4 0 - 1 3 - 2 3 - 10 . (b) x = A - 1 b = - 1 1 - 4 0 - 1 3 - 2 3 - 10 2 3 4 = - 2 + 3 - 16 - 3 + 12 - 4 + 9 - 40 = - 15 9 - 35 .

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Winter 2006 - Nagy's Class - Exam 1 (Version B) - Print...

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