8.45 (a), §2 Solution

Eigenvalues:

There are two roots: and

The 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. To get simple numbers, take v_1y = -2, then v_1x = 3:

Check:

The eigenvector corresponding to satisfies

Solving using Gaussian elimination:

Choosing v_2y = 1, then v_2x = -2:

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