In Problems 3133 A represents a 2 x 2 matrix. (a) Show that if A has the repeated eigenvalue with two linearly independent associated

In Problems 31–33 A represents a 2 x 2 matrix.

(a) Show that if A has the repeated eigenvalue λ  with two linearly independent associated eigenvectors, then every nonzero vector v is an eigenvector of A.

(b) Conclude that A must be given by Eq. (22). (In the equation Av = λv take v = [1  0]^T and v = [0  1]^T.)

07 A=a[& #]=[@ 4] (22)