Let A be a matrix and x be a non-zero vector such that
A x = 2 x.
Then we have that
A^7 x = a x
some value of a. What is a equal to?
\(A x = 2x\\ A^7x = A^6(Ax) =\\ A^6 (2x) = \\ 2 A^5(Ax) = 4 A^5 x\\ \text{etc. See if you can finish}\)
i got the wrong answer. Do you know what the correct one is?
