Linear Algebra Solutions 77

Linear Algebra Solutions 77 - The eigenvectors...

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The eigenvectors corresponding to an eigenvalue λ are the non–zero vec- tors [ x, y ] t satisfying 0 - λ 2 2 - 3 - λ ‚• x y = 0 0 . λ 1 = - 4 gives equations 4 x + 2 y = 0 2 x + y = 0 which has the solution y = - 2 x . Hence x y = x - 2 x = x 1 - 2 . A corresponding unit eigenvector is [1 / 5 , - 2 / 5] t . λ 2 = 1 gives equations - x + 2 y = 0 2 x - 4 y = 0 which has the solution x = 2 y . Hence x y = 2 y y = y 2 1 . A corresponding unit eigenvector is [2 / 5 , 1 / 5] t . Hence if P = " 1 5
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