- #1

karnten07

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## Homework Statement

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

## Homework Equations

## 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 I am 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 I am 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 I've missed a trick or something. I've searched on the internet for examples and methods but their seems to be so many and i can't 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