Need some help with this, the book is written in a very confusing way. I'm following the examples exactly and not getting the correct result.
The matrix A = [2,-1 ; -1,2]
I found the two eigenvalues, to be λ = 1 and λ = 3
Now when I do the A - λI calculation and reduce the matrix I get
for λ = 1
x1 + x2 = 0 --> x1 = -x2
however, the solution in the book says the answer is
for λ = 3
-x1 + x2 = 0 --> x1 = x2
but again, the solution says
Can someone please clarify or point out what I am doing wrong?