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$\begingroup$

Where $B$ is the matrix: $$ \begin{pmatrix} 1 &1 &k\\ 2 &k &1 \\ k &2 &2 \end{pmatrix} $$

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    I would swap rows so that the last becomes the first one. Then I'd apply Gauss' reduction.2012-09-18
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    Roxana, are you saying that you know how to bring a matrix to reduced row-echelon form, but that you don't know how to read off the solutions once you've done that?2012-09-18
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    Gerry, would I be right in saying that where k=1, x1+x4=0 and x2+x3=0 so that there are infinitely many solutions but there are no solutions where k=2 and k=-3?2012-09-18
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    @Roxana Why do you have four unknowns?2012-09-18
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    Sorry, would x1=1 and x2+x3=0 be correct?2012-09-18
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    Yes, that's correct for $k=1$. If you want to be sure I see a comment directed to me, you have to write @Gerry.2012-09-19

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