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Let \(\mathbf{A}\) be a matrix, and let x and y be linearly independent vectors such that

\(\mathbf{A} \mathbf{x} = \mathbf{y}, \mathbf{A} \mathbf{y} = \mathbf{x} + 2\mathbf{y}\)

Then we have that

\(\mathbf{A}^5 \mathbf{x} = a \mathbf{x} + b\mathbf{y}\)

for some scalars a and b. Find the ordered pair (a,b).

Guest Feb 19, 2019