# Pythagorean Generator Matrix

$\begin{pmatrix}x & y & y \\ y & x & y \\ y & y & z \end{pmatrix}\begin{pmatrix}a \\ b \\ c \end{pmatrix} = \begin{pmatrix}a' \\ b' \\ c' \end{pmatrix}$ If the above equation holds true, then there exist coprime positive integers $$x, y, z$$ such that any Pythagorean triple $$(a, b, c)$$ produces another Pythagorean triple $$\big(a', b', c'\big).$$

Find the sum of such $$x, y,$$ and $$z.$$

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