Describe all solutions to ax = 0 in parametric vector form, where a is row equivalent to the given matrix.

Describe all solutions of Ax=0
in parametric vector form, where A
is row equivalent to the given matrix.

⎡⎣⎢⎢⎢1000−20003000−610054000−610⎤⎦⎥⎥⎥

I know that I should get this into row reduced echelon form, but I'm having trouble doing so. I attempted it below.

⎡⎣⎢⎢⎢1000−20003000−610054000010⎤⎦⎥⎥⎥

⎡⎣⎢⎢⎢1000−200030000100294000010⎤⎦⎥⎥⎥

I'm not quite sure where to go from here, also I don't know how I would describe all solutions of Ax=0
.
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asked
Jan 27 '13 at 17:41

ground.clouds1
339●3●6●13 edited
Jan 13 '16 at 13:42

Martin Sleziak
40.3k●5●102●219

But it is already in echelon form. Isn't it? – Tomas Jan 27 '13 at 17:52

As a hint, try multiplying your above matrix, by a vector with six variables, say x,y,z,r,s,t
and you'll find out what x
is equal to, what r
is equal to, and what t
is equal to. – CodyBugstein Jan 27 '13 at 17:57

@Tomas For reduced echelon form, the first entry in each row must be the only entry in its column, so the original matrix isn't quite there yet. – icurays1 Jan 27 '13 at 17:58

@Tomas what? My matrix is telling me 0=1
which would make it inconsistent. – ground.clouds1 Jan 27 '13 at 17:59
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Think about what