(2 - L)^2 - 4 = 0 is the characteristic polynomial.
can someone explain to be how they get the eigenvectors for the following matrix
however answers says when
i don't understand how they got this result, someone please explain this to me.
You are making two errors. The first is in thinking that the row reduced matrix leads to . This really the reduced form of the "augmented matrix"
for solving the matrix equation .
That is, it corresponds to the equation so that you get , not .
Your second error is in thinking you can set v2= 1 to get (using the correct ) and then set to get . You can do one or other, not both! If you set v2= 1, you get v1= 1/2 and so have the eigenvector . If you take v1= 1, you get v2= 2 and so have the eigenvector .
Since one is a multiple of the other, both are eigenvectors corresponding to eigenvalue 4.