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# tutorial7 - Answer If 2 a 3 b-c = 0 then the system is...

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Tutorial #7 - MAT 1332A - Fall 2009 November 2, 2009 Section 5.5: question 12 Let z 1 = 5 - 4 i , z 2 = 4 + 3 i , and z 3 = 1 + i . Find: (a) ( z 1 + z 2 ) z 3 (b) z 1 - z 2 z 3 (c) | 3 z 1 - 2 z 2 | Use Gaussian elimination to ﬁnd the solution of the system: x 1 - 2 x 2 + x 3 = 0 2 x 2 - 8 x 3 = 8 - 4 x 1 + 5 x 2 + 9 x 3 = - 9 Answer : (29 , 16 , 3) is the unique solution. 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 Find conditions (if possible) on the numbers a , b and c so that the system has no solution, a unique solution, or inﬁnitely many solutions.
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Unformatted text preview: Answer : If 2 a + 3 b-c = 0 , then the system is consistent with inﬁnitely many solutions. Otherwise, if 2 a + 3 b-c 6 = 0 , the system is inconsistent. The system cannot have a unique solution, no matter what a , b and c are. Therefore, there is no condition on a , b and c for which the system has a unique solution. 1...
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