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vic9317


Newbie


Joined: 16 Nov 2008
Posts: 26

Posted: 08 Nov 2010 06:20:05 pm    Post subject:

I was asked a question that I can't seem to figure out concerning the row echelon form of a matrix and the ref( command.

Take the following matrix [A], for example:

[1 3 -5 ]
[4 7 -10]
[-2 2 3 ]

Using ref([A])►Frac on it produces the following:

[1 7/4 -5/2 ]
[0 1   -4/11]
[0 0   1    ]

However, manually finding the row echelon form as well as using online solvers such as this one produces:

[1 3 -5]
[0 1 -2]
[0 0  1]

My question is: why? Does the calculator's method of finding the ref (which I presume is Gaussian elimination) different from the manual method? Are they both correct?

Seems intriguing...
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Weregoose
Authentic INTJ


Super Elite (Last Title)


Joined: 25 Nov 2004
Posts: 3976

Posted: 09 Nov 2010 04:10:47 pm    Post subject:

Safety measures included, this is the exact algorithm used by that solver to generate its matrices on the right hand side.

dim([A]→L1
[A]
For(U,1,min(L1
If not(Ans(U,U
Pause rowSwap(Ans,U,U+1►Frac
Pause *row(Ans(U,U)‾¹,Ans,U►Frac
For(V,U+1,L1(1
If Ans(V,U
Pause *row+(‾Ans(V,U),Ans,U,V►Frac
End
End

That's all I can provide at this moment. It's been a long time since I've last worked with matrix operations.


Last edited by Guest on 09 Nov 2010 04:11:55 pm; edited 1 time in total
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