Question

Consider the given matrix.

−1		2
−5		1

Find the eigenvalues. (Enter your answers as a comma-separated list.)

λ = 3i,−3i

(I got these right)
Find the eigenvectors of the matrix. (Enter your answers in order of the corresponding eigenvalues, from smallest to largest by real part, then by imaginary part.)

K1 =				K2 =

I can't seem to get the eigenvectors right.

Answer 1

Here the Eigen values are complex, so the Eigen vectors are also complex.

After forming the equations, we try to make both the equations same, so that we get relation between the values in Eigen vector.

We put an arbitrary value to one of the variable, and find the value of other variable.

Note : Always remember that Eigen vectors are always non zero. Don't consider trivial solution (0,0) for the system of equations formed.