Clear[A, x]
A = {{2, -1, 0}, {0, 2, -1}, {0, -1, 2}};
MatrixForm[%]
vx = {0.5, 0.5, 1.1};
Do[vy = A.vx;
Print[k, " ", vy, " ", vy[[1]]/vx[[1]], " ", vy[[2]]/vx[[2]]];
vx = vy/Max[Abs[vy]], {k, 1, 15}]
Eigensystem[A]
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