Suppose Ax x with x 0 Let a be a scalar different from the eigenvalues of A, and let B (A a1) 1 Sub tract ax from both sides of the equation Ax x, and use algebra to show that 1 ( a) is an eigenvalue of B, with x a corresponding eigenvector

Question: Suppose Ax = x with x 0. Let a be a scalar different from the eigenvalues of A, and let B = (A -a1)-1.

Suppose Ax = λx with x ≠ 0. Let a be a scalar different from the eigenvalues of A, and let B = (A -a1)-1. Sub-tract ax from both sides of the equation Ax = λx, and use algebra to show that 1/ (λ - a) is an eigenvalue of B, with x a corresponding eigenvector.

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