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Exercise 32.2

Perform Gaussian elimination on the following set of equations to find a solution

x + 3 y − z = 7 3 x + y − 2 z = 4 − x − y + z − 1

Solution:

Here if you add the first and third equations you are lucky to find that the sum equation is 2 y = 8 , and you deduce y = 4 . Adding the second and twice the third equation yields x − y = 6 , or x = 10 . Substituting in the third equation you find − 10 − 4 + z = 1 which tells you z = 15 , and you have your solution. Testing the solution in the original equations you get 10 + 12 − 15 = 7 , 30 + 4 − 30 = 4 , and − 10 − 4 + 15 = 1 , which are all correct.

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