(a) Show that if A has the repeated eigenvalue 1 with two linearly independent associated eigenvectors, then every nonzero vector v is an eigenvector of A. (Hint: Express v as a linear combination of the linearly independent eigen- vectors and multiply both sides by A.) (b) Conclude that A must be given by Eq. (22). (Suggestion: In the equation Av = Av take v = [1 0]' and v = [0 1]'.)

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