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I have an assignment question that I am having some hard time working out and would appreciate any help understanding and solving this please. Here is the question

Let $L:\mathbb{R}^3\to\mathbb{R}^3$ be given by $$(x; y; z)^T \mapsto (x - y; y - z; z - x)^T$$ Find the matrix $A$ of $L$ with respect to the basis: $$(-1; 0; 1)^T ; (1; 1; 1)^T ; (0; 1; 0)^T$$ Then find the matrix $B$ of $L$ with respect to the basis: $$(0; 0; 1)^T , (0; 1; 1)^T , (1; 1; 1)^T$$ Finally, find a matrix $P$ so that $$B = P^{-1}AP$$

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    Oops, sorry, I didn't see you edited it already. :)2011-07-15

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