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hw_sol(5_1)

# hw_sol(5_1) - A-1 from the left on both sides(c Add x on...

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Section 5.1 12 Find the eigenvalues and eigenvectors of A = " 3 4 4 - 3 # and A = " a b b a # . 16 If A is the 4 by 4 matrix of ones, find the eigenvalues and the determinant of A - I . 24 What do you do to Ax = λx , in order to prove (a), (b) and (c)? (a) λ 2 is an eigenvalue of A 2 , (as in Problem 22). (b) λ - 1 is an eigenvalue of A - 1 , (as in Problem 21). (c) λ + 1 is an eigenvalue of A + I , (as in Problem 20). Solution. (a) Multiplying A from the left on both sides; (b) Multiplying
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Unformatted text preview: A-1 from the left on both sides; (c) Add x on both sides, and view x on the left hand side as Ix , where I is the identity. 36 Find the eigenvalues of A , B and C : A = 1 2 3 0 4 5 0 0 6 , B = 0 0 1 0 2 0 3 0 0 , and C = 2 2 2 2 2 2 2 2 2 . 1...
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