]> Exercise 32.2

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.