Up: 9.56(a) Previous: 9.56(a), §1 Asked

9.56(a), §2 Solution

Given:

Eigenvalues:

There are two roots:

and

The eigenvector corresponding to satisfies

Taking v₁_y = -2, then v₁_x = 1, giving an eigenvector (1,-2). Normalizing this vector to length one gives:

The eigenvector corresponding to satisfies

Taking v₂_y = 1, then v₂_x = 2, giving after normalization:

Finally:

Check:

The diagonal form is what matrix A looks like in the coordinate system x',y' shown below:

Up: 9.56(a) Previous: 9.56(a), §1 Asked