Digital Paint Discussion Board
Digital Paint Community => Other Stuff => Topic started by: Ace on March 11, 2015, 03:41:25 AM
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So I'm doing an a bit of a pre-assessment for something, and I feel like I am missing something on this question:
Solve the following and explain your answer:
x1 - 2x2 + 3x3 = 0
-2x1 - 3x2 - 4x3 = 0
2x1 - 4x2 + 4x3 = 0
Now I know how to solve a normal 3 variable system, but with this, since they are all set to 0, how exactly would I solve it? Or would I just solve it by saying that there are an infinite number of solutions since any variable == 0 would mean the other two could be anything. Maybe I'm just brain farting, but some help would be sweet.
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I remembered I studied this months ago but forgot it 3 months later.
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Should only be the trivial solution of x1=x2=x3=0. You would get more than one solution if you had a free variable, but that isn't the case here. Also just for the sake of it in mathematica:
Solve[x - 2 y + 3 z == 0 && -2 x - 3 y - 4 z == 0 && 2 x - 4 y + 4 z == 0, {x, y, z}]
{{x -> 0, y -> 0, z -> 0}}
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Isn't just the exact solution 0? What method did you use for solving it? There are quite a few methods, simplest being discriminant method and maybe gaussian elimination.
I tried solving it with gaussian and came up with sth like this
1 -2 3 0
-2 -3 -4 0
2 -4 4 0
1. line * 2 -> 2 -4 3 0
switch 1. line and 2. line
-2 -3 -4 0
0 -7 6 0
0 -7 7 0
-2 -3 -4 0
0 -7 6 0
0 0 1 0
z = 0
y = 0
x = 0
Might be wrong, did it during a lecture lol, i went through some online equation solvers and they all came up with 0 too.
The only question i have is if it isn't some kind of 'exception' as in 1=0, but i doubt it
EDIT:Agreed with Cameron
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Thanks guys, I was using Gaussian and got the same answers, but I just thought I was missing something, seemed too simple.