(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the eigenvalues and eigenvectors of A

1 1 a

1 -1 b

0 0 1

you can assume a and b are not equal to zero

2. Relevant equations

3. The attempt at a solution

Using det(A-sI) = 0 where s is the eigenvalue

i get (s^2 - 2)(1 - s) = 0

therefore giving s1 = 1 and s2/3 = +/- 2

Id be very grateful if someone could check this is correct because im a little uncertain.

From here i struggle to find the eigenvectors, i substitute the eigenvalues to (A-sI) to get

0 1 a

1 -2 b

0 0 0

Then i saw a method where i equated the sum of this matrix with (x, y, z) - a vector written vertically, to (0,0,0) also written vertically.

From that i get y + za = 0, x - 2y + bz = 0

But then i get lost in the method from here because im unsure i can apply it to this case. In fact i think i may have gone about finding the vectors in the complete wrong way, or ive missed a trick or something. Ive searched on the internet for examples and methods but their seems to be so many and i cant seem to decipher which ones i can use or even how to use them. So any help at all would be greatly appreciated, preferably before tuesday morning as that is when it is due. Many thanks

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# 3 x 3 matrix eigenvectors

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