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November 23rd, 2008, 03:39 PM   #1
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Homework question

The directions state:

Find the solution space of the following systems of linear homogeneous equations:

x-y+z-w=0
2x+y-z+2w=0
2y+3z+w=0

Is this the same as finding the solutions, because I did that and got (-z, -3z, 3z, z). But I don't know what a solution space is. Help. Thanks you so much.
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November 24th, 2008, 04:33 PM   #2
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Re: Homework question

To answer my own question:

the solution space is actually the subspace you get. For instance, this problem yields a one dimensional subspace.
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December 2nd, 2008, 07:45 PM   #3
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Re: Homework question

I don't think that solution set is right.

The vector -1,-3,3,1 does not give you 0 when used as weights in the original equation. It is a system of 4 unknowns in 3 rows there has to be a free variable somewhere.

The solution (-1,-3,3,1) does not satisfy ax=0.

That is if you still care about this problem :P, unless im missing something..
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December 7th, 2008, 08:04 AM   #4
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Re: Homework question

Oh, wow, I completely missed this problem...

Anyway, yes, the vector (-1,-3,3,1) forms a basis for the vector space. It isn't the solution itself--- z is the free variable.

So, undermine, you are missing something
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April 15th, 2015, 09:35 PM   #5
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Thanks! Looking forward to it. I think I've spend more time watching your show this at work than actually working! Fantastic stuff!
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April 16th, 2015, 05:17 PM   #6
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Quote:
Originally Posted by orionankh View Post
The directions state:

Find the solution space of the following systems of linear homogeneous equations:

x-y+z-w=0
2x+y-z+2w=0
2y+3z+w=0

Is this the same as finding the solutions, because I did that and got (-z, -3z, 3z, z).
This makes no sense because you haven't said what variables each of those places means. Normally, I would assume (x, y, z, w) since that is the order of the variables in the equations. But x= -z, y= -3z, z= 3z, w= z makes no sense.
Quote:
But I don't know what a solution space is. Help. Thanks you so much.
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April 16th, 2015, 06:04 PM   #7
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Quote:
Originally Posted by Country Boy View Post
This makes no sense because you haven't said what variables each of those places means. Normally, I would assume (x, y, z, w) since that is the order of the variables in the equations. But x= -z, y= -3z, z= 3z, w= z makes no sense.
You are aware that this thread is seven years old? It was triggered by a troll.

-Dan
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