223midterm20099 - University of Toronto Department of...

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Unformatted text preview: University of Toronto Department of Mathematics MAT223H1F Linear Algebra I Midterm Examination October 22, 2009 H. Kim, S. Kudla, F. Murnaghan, S. Uppal Duration: 1 hour 50 minutes Last Name: Given Name: Student Number: Tutorial Code: No calculators or other aids are allowed. FOR MARKER USE ONLY Question Mark 1 /6 2 /10 3 /10 4 /10 5 /10 6 /10 7 /4 8 /5 TOTAL /65 1 of 9 [6] 1. Find all solutions of the homogeneous linear system Ax = 0, where A is a 3 6 matrix whose reduced row echelon form is 1 2 0 3 0 5 0 0 1 4 0 6 0 0 0 0 1 1 . Express your answer in parametric form. 2 of 9 [8] 2. Find a 2 2 matrix A such that A 1 2- 1 0 = 3 1 2 3 . 3 of 9 [10] 3. Let A = 3 4 5 3 1 1 1 1 1 2 3 1 3 5 7 3 . Find a non-singular (invertible) matrix U such that R = UA , where R is the reduced row echelon form of A . 4 of 9 [10] 4. Let P 4 ( R ) be the vector space of all real valued polynomials of degree less than or equal to four. Let W be the subspace of...
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This note was uploaded on 02/12/2012 for the course MATH 223 taught by Professor P during the Spring '11 term at University of Toronto- Toronto.

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223midterm20099 - University of Toronto Department of...

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