(a) Show that if A has the repeated eigenvalue with two
Chapter , Problem 33(choose chapter or problem)
(a) Show that if A has the repeated eigenvalue 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 eigenvectors and multiply both sides by A.) (b) Conclude that A must be given by Eq. (22). (Suggestion: In the equation Av D v take v D 1 0 T and v D 0 1 T .)
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