I'm hoping someone can come along and give me a tap on the head for being so silly, but i've been trying this problem *all day* and i just cant seem to get a correct answer, even when checked with other people, we're all stumped! What we have:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]3x - 2y + 5z = 0[/itex]

[itex]x + y + 5z = 5[/itex]

[itex]x - 2y - z = -4[/itex]

I've then put this into an augmented matrix, and converted to reduce row echelon form which gives me these equations:

[itex]x + z = 2[/itex]

[itex]y + z = 3[/itex]

So I try a general solution set as (t, 1+t, 2-t) however it doesn't seem to work with the equations at the beginning. so i looked at what i'd written and went back a step before row echelon form which has these equations:

[itex] x + y + 5z = 5[/itex]

[itex] y + z = 3[/itex]

Giving a solution set of (4t-10, t, 3-t) but still this doesn't seem to be consistent. Any ideas where im going wrong? Thanks :)

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# System of linear equations

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