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# tut2 - MATH 1104F Solutions to Tutorial assignment 2 Total...

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MATH 1104F - Solutions to Tutorial assignment 2 January 19, 2010 Total: 10 points 1. Consider the following system: 2 x 1 - 3 x 2 - 3 x 3 = a - x 1 + x 2 +2 x 3 = b x 1 - 3 x 2 = c (a) [2.5 points] Find conditions (if possible) on the numbers a , b and c so that the system has no solution, a unique solution, or in±nitely many solutions. (b) [2.5 points] Find speci±c values for a , b and c for which the system has in±nitely many solutions. Using these values, identify the basic and the free variable(s) of the corresponding system. Then describe the solutions parametrically. Solution: (a) 2 - 3 - 3 | a - 1 1 2 | b 1 - 30 | c R 1 R 3 1 - | c - 112 | b 2 - 3 - 3 | a R 2 R 2 + R 1 R 3 R 3 - 2 R 1 1 - | c 0 - 22 | b + c 03 - 3 | a - 2 c R 2 ←- ( 1 2 ) R 2 1 - | c 01 - 1 | - ± b + c 2 ² - 3 | a - 2 c R 3 R 3 - 3 R 2 1 - | c - 1 | - ± b + c 2 ² 0 0 0 | 2 a +3 b - c 2 If 2 a b - c = 0, then the system is consistent with in±nitely many solutions. Otherwise, if 2 a b - c ± = 0, the system is inconsistent. The

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tut2 - MATH 1104F Solutions to Tutorial assignment 2 Total...

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