223midterm20141sol - University of Toronto Department of...

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University of Toronto Department of Mathematics MAT223H1S Linear Algebra I Midterm Exam I February 14, 2014 A. Garcia-Raboso, C. Kent, F. Murnaghan, K. Tyros, S. Uppal Duration: 1 hour 50 minutes Last Name: Given Name: Student Number: Email (@mail.utoronto.ca): Instructions : No calculators or other aids are allowed . Show all your work and justify your answers . You may use the back of each page for rough work but all your answers must be written on the front of each page . 1 of 8
1. Suppose that the given matrix is the augmented matrix of a system of linear equations in the variables x 1 , x 2 , x 3 , x 4 , x 5 . 1 1 - 2 3 - 4 1 0 1 1 2 - 5 0 0 0 0 1 - 2 0 [4] (a) Find the reduced echelon form of the given system.
[2] (b) Identify the free variables.
[4] (c) Find the set of solutions to the given system.

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