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! :)
Found 3 solutions by mathmate, MathTherapy, ikleyn:
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.
Answer by MathTherapy(10680)  (Show Source):
Answer by ikleyn(53538)  (Show Source):
You can put this solution on YOUR website! .
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! :)
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Use advantages of the modern technology.
Go to web-site www.reshish.com
Find there free of charge online calculator for solving systems of linear equations.
Choose the Gauss-Jordan elimination method there.
Setup the extended matrix of the system and get the step by step solution
with all accompanying detailed explanations
x = 1, y = 0, z = 3, w = 2.
Tutor @mathmate reviewed this problem and gave his interesting suggestions.
One of his suggestion was that the matrix of the system is ill-defined.
I checked it by calculating its determinant.
(Again, I used the online calculator www.reshish.com)
The determinant of the matrix is 54, so it is NOT ill-defined.
@ikleyn, PhD in Math and Physics,
with a professional Math education from a renowned university and
with 40 years experience working as a computer programmer
and a researcher in computational physics/mechanics/civil engineering.
(solid bodies, porous media, heat transfer (thermal conductivity, phase changes, convective heat transfer,
combined thermal, convective and radiative heat transfer, hydrodynamics, fluid-structure interaction etc.)
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