Eigenvalues:
There are two roots: andThe eigenvector corresponding to satisfies
Solving using Gaussian elimination:
Equation (1) gives . In order to get a vector, instead of a set of possible vectors, one component must be arbitrarily chosen. Remember: undetermined constants in eigenvectors are not allowed. To get simple numbers, take v1y = -2, then v1x = 3:Check:
Note: the null space of the matrix above is
so would also have been an acceptable eigenvector, just messier.The eigenvector corresponding to satisfies
Solving using Gaussian elimination:
Choosing v2y = 1, then v2x = -2: