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My professor assigned us this homework for a separate text book from our own. I am very lost on how to approach this problem. While our text covers homogeneous matrices none are the examples are like anything in the context of this problem. I was hoping someone could point me to a resource that would be helpful in attacking this problem.

The first transformation I got: A^0_1 =

\left[ {\begin{array}{cc} -1 & 0 & 0 & 0 \ 0 & 0 & -1 & C+E \ 0 & -1 & 0 & A-D \ 0 & 0 & 0 & 1 \

\end{array} } \right] But for the second I get confused, I get: A^1_2 =

\left[ {\begin{array}{cc} 0 & -1 & 0 & B \ 0 & 0 & -1 & A-D \ 1 & 0 & 0 & 0 \ 0 & 0 & 0 & 1 \

\end{array} } \right]

Thanks!

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    My comment was indeed talking about$0$wrt 2, which was why I deleted it. I've given a demonstration of how to compute $A_2^1$, tell me if it helps or if you don't grasp it fully.2011-09-22

1 Answers 1

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So apparently my initial assumption that the coordinate system remains the same for each matrix is false, and your matrix for $A_2^1$ is correct after all. Let's look at $A_3^2$ this time. The transformation maps $e_1\to-e_3,$ $e_2\to e_2,$ $e_3\to e_2.$ Mapping $e_i$ to $e_j$ means the $i$-th column of the $3\times3$ part is $e_j$ (so that $T(e_i)=e_j$). Any negative signs get multiplied for the final column. So we get $\begin{pmatrix}-e_3&e_2&e_1\end{pmatrix}=\begin{pmatrix}0&0&1\\0&1&0\\-1&0&0\end{pmatrix}.$ Now the displacement vector from point 2 to point 3 is $(e,0,a)$, so the final matrix is $T=\begin{pmatrix}0&0&1&e\\0&1&0&0\\-1&0&0&a\\0&0&0&1\end{pmatrix}.$

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    Awesome, I glad we were able to get trudge through this! If I could, I'd give you$2$up votes for sticking with me :)2011-09-22