Suppose and are 2x3 row -reduced echelon matrices and that the systems and have exactly the same solutions. Prove that

Can anyone give me any hint to start the proof?Thanks.

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- Aug 29th 2011, 07:18 PMproblemRow-reduced echelon matrix
Suppose and are 2x3 row -reduced echelon matrices and that the systems and have exactly the same solutions. Prove that

Can anyone give me any hint to start the proof?Thanks. - Aug 30th 2011, 04:25 AMFernandoRevillaRe: Row-reduced echelon matrix
Try by contradiction: if then ...

- Aug 30th 2011, 06:29 AMproblemRe: Row-reduced echelon matrix
Can I claim that suppose one of the entries in both R and S are not the same, then using the same solution, claim that there is a contradiction and actually the entry(that I had supposed not the same) is the same?

That is suppose both R and S have the same second row but different first row with the 1,1 and 1,2 entries the same but 1,3 entry differs. Let the 1,3 entries of R and S be r and s respectively. Then if we have a solution and , we will have . But I am stucked here as if is zero, then my argument does not create contradiction. - Aug 30th 2011, 07:35 AMFernandoRevillaRe: Row-reduced echelon matrix
If then, because they have different dimensions. Analyze the cases . For example and

- Aug 30th 2011, 07:59 AMbondesanRe: Row-reduced echelon matrix
I think that if then RX-SX=0 => X=0 or R-S=0, which means that R=S because of our assumption that .

- Aug 30th 2011, 08:13 AMFernandoRevillaRe: Row-reduced echelon matrix
- Aug 30th 2011, 08:21 AMproblemRe: Row-reduced echelon matrix
Hi FernandoRevilla,

The R and S that you had given are in row-reduced form and the X that is given by you is also a solution for RX=0 and SX=0. Does this mean that what I want to prove(the initial question) is not correct? - Aug 30th 2011, 08:30 AMFernandoRevillaRe: Row-reduced echelon matrix