Question

How to find eigenvector when eigenvalue is given?

Answer 1

Step-by-step explanation:

If u is an eigenvector of A and λ is the corresponding eigenvalue, you know the following:

Au=λu

So in your example, you can do the following (I’ll take the second one):

Au2=⎛⎝⎜320−11−1−1−22⎞⎠⎟⎛⎝⎜101⎞⎠⎟=⎛⎝⎜202⎞⎠⎟=2u2

So λ2=2. Do the same for u1 and u3.