I was only using 2^n and 3^n as an example. (a) I couldn't remember the exact formula, and (b) it was a messy formula, which only clouded the basic issue.

The student stumbled around the "parentheses around the 34s" solution.

The relative tolerance was causing other problems. With the seed I gave you, the matrix A has the property that A^2 has two entries which are exactly zero. If students round off their answers (say, 1/3 to 0.3333333333), using relative tolerance will tell them that their answer is wrong.

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