18.06 Problem Set 7 - Solutions

Problem 3: (12=3+3+3+3) Let A = 1 4 2 3 . (a) Find all eigenvalues and corresponding eigenvectors of A. Solution The characteristic equation is λ2 −4λ−5 = 0, thus the eigenvalues are λ 1 = 5,λ 2 = −1. For λ 1 = 5, the eigenvector v 1 is a solution to −4 4 2 −2 v 1 = 0, which implies v 1 = 1 1 . For λ 1 = −1, the eigenvector v ...

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