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# help appreciated

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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 = Y x some value of a. What is Y equal to?

Jul 6, 2019

$$\text{I'm going to assume you're not at the point where you are diagonalizing matrices yet}\\ \text{So what they probably want you to do is notice that}\\ A^7 x = A^6 A x = A^6 2x = 2 A^5 Ax = 4A^5x ~\text{ etc.}\\ \text{see if you can work the whole thing through and find Y}$$