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Linear Algebra - Reducing to Row Echelon Form.

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kj_:

--- Quote from: squance on January 06, 2009, 09:40:13 pm ---Sorry for double posting.
But I finally got the right answer!!! YES! (after several hours of pain.... :( )
But if anyone has the answers to the questions at the bottom of my first post, that would be great

--- End quote ---

If I'm interpreting you correctly, I think it would make a difference - as it doesn't fit the definition of row echelon form. Row echelon form = leading 1 as coeffs going diagonally, and 0's under it?

EDIT: I re-read your initial question, and if you mean you want to place the x + y - 4z = 30 as row 1, and 3x + 2y - z = -15 as row 2, then no, it wouldn't make a difference. You would get the same answer.
(This is actually just a row-swap, which is legit in a matrix)

squance:
Hmm...I'm not sure. I think the row echelon form you are talking about is the "reduced echelon form" because in my case I don't have to have any leading 1's...

And the unique solutions I got are x = -4, y = 2 and z = 7 :)

kj_:

--- Quote from: squance on January 06, 2009, 09:52:55 pm ---Hmm...I'm not sure. I think the row echelon form you are talking about is the "reduced echelon form" because in my case I don't have to have any leading 1's...

And the unique solutions I got are x = -4, y = 2 and z = 7 :)

--- End quote ---

What I've been taught, generally row echelon form has all leading 1's, whereas reduced row echelon form has all leading 1's and 0's otherwise only, barring the last column. (which is of course your solution to the coeff :P)

squance:
Oh ok.
Thanks for that. I think I'll go and ask my lecturer next time at uni because he hasn't made it clear for me.

Mao:

--- Quote from: kj_ on January 06, 2009, 10:02:24 pm ---
--- Quote from: squance on January 06, 2009, 09:52:55 pm ---Hmm...I'm not sure. I think the row echelon form you are talking about is the "reduced echelon form" because in my case I don't have to have any leading 1's...

And the unique solutions I got are x = -4, y = 2 and z = 7 :)

--- End quote ---

What I've been taught, generally row echelon form has all leading 1's, whereas reduced row echelon form has all leading 1's and 0's otherwise only, barring the last column. (which is of course your solution to the coeff :P)

--- End quote ---

that's more of a 'preferred' thing, and it looks a lot nicer.

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