Consider the system of linear equations x + cy - z =...

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University of Toronto Department of Mathematics MAT223H1S Linear Algebra I Midterm Examination I Feb. 10, 2011 M. Czubak, A. Macleod, B. Smithling, S. Uppal Duration: 1 hour 30 minutes Last Name: Given Name: Student Number: Tutorial Code: No calculators or other aids are allowed. FOR MARKER USE ONLY Question Mark 1 /10 2 /10 3 /10 4 /10 5 /5 6 /5 TOTAL /50 1 of 8 DownloaderID 21140 ItemID 4524 Item ID: 4524 Item ID: 4524 Item ID: 4524
1. Consider the system of linear equations x + cy - z = 1 - x + ( c - 2) y + z = - 1 2 x + 2 y + ( c - 2) z = 1 Find all values of c R such that the system has (i) no solution, (ii) a unique solution, or (iii) infinitely many solutions.

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