Question 938535: Hello, I am having issues with my system of equations homework. I was wondering of you could help me. I generally know how to solve them but I cannot get mine to turn out.
The system is:
x+y+z+w=6
2x+3y-w=0
-3x+4y+z+2w=4
x+2y-z+w=0
Thanks in advance! :)
Answer by mathmate(429)   (Show Source):
You can put this solution on YOUR website! Generally this would be solved using Gaussian Elimination followed by a backward pass. It is rather lengthy to explain the solution of a 4x4 step by step. Instead, I would refer you to some reliable sources for the details:
http://mathworld.wolfram.com/GaussianElimination.html
http://en.wikipedia.org/wiki/Gaussian_elimination
http://www.purplemath.com/modules/systlin6.htm
I have solved the system using my own solver, image follows.
Note that if we round to about 14 digits (avoiding the effects of the rms error), we get as solution (1,0,3,2) which you could back substitute readily to confirm that the solution is exact.
Also, a large value of the rms error indicates ill-conditioning, and requires some pivoting operations. Since this solution consists of integers and may be verified to be exact, there is no such problem for the present problem.
Finally, if you prefer to learn step-by-step the solution of a system of linear equations using Gaussian Elimination, please ask a new question to that effect, perhaps using a 3x3 instead of a 4x4.
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