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## Homework Statement

Suppose [itex]x_{1} = \begin{pmatrix}

2 & 9 & 6 \\

\end{pmatrix}\begin{pmatrix}

3 & 5 & 8 \\

\end{pmatrix}\begin{pmatrix}

4 & 7 \\

\end{pmatrix}[/itex] and [itex]x_{2} = \begin{pmatrix}

1 & 5 & 9 \\

\end{pmatrix}\begin{pmatrix}

2 & 7 & 6 \\

\end{pmatrix}\begin{pmatrix}

3 & 4 \\

\end{pmatrix}.[/itex]

Determine the conjugate a, so that x

_{1}= ax

_{2}a

^{-1}.

## The Attempt at a Solution

I know the solution is a = (1 6 8)(2 3 7 5), since we did this in class. However, we didn't really explain how we got to this solution. And I can do conjugates where you just line up the cycles one under the other, but this method doesn't work here, because, say 1 does not get sent to 2, and 5 not to 9, as you'd assume if you just wrote (1 5 9) above (2 9 6).

I really want to figure this out, but this example really puzzles me, as I haven't yet found the general method, and the fact that x

_{2,i}= a(x

_{1,i}) doesn't really help me here.

Anyways, any help here would be greatly appreciated.

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