Solving Eigenvector Order Homework

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The discussion revolves around finding eigenvectors for a given matrix A with eigenvalues 6 and 1. The user initially expresses confusion regarding the order of the eigenvectors, as their results differ from those listed in the textbook. After attempting to solve for the eigenvectors, they realize the discrepancy was due to a misreading of the book. Ultimately, the user finds the correct eigenvector order and resolves their question. The thread highlights the importance of careful reading in mathematical problem-solving.
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Homework Statement



A =
2 -2
-2 5

Eigenvalues are: 6, 1

Find eigenvectors. My only question is about order. My book lists them in the opposite order as I and I am not sure where I went wrong.

Homework Equations



A =
2 -2
-2 5

Eigenvalues are: 6, 1

The Attempt at a Solution



i..e for 1:
1λ1 -2λ2 = 0
λ1 = 2λ2
= (2λ2)/(λ2)

Let λ2 = 1

= 2/√5, 1/√5

Yet my book lists them as 1/√5, 2/√5. Why is this?
 
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EDIT: Never mind, I was misreading the book. Answer found.
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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