Homework 5 - UMass Math
... (b) find a permutation of the columns of F that produces F , so that F P = F ; (c) use these to find F 2 and F 4 . ...
... (b) find a permutation of the columns of F that produces F , so that F P = F ; (c) use these to find F 2 and F 4 . ...
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... 16. Suppose that A is a 6 × 6 matrix with characteristic polynomial cA (λ) = (1 + λ)(1 − λ)2 (2 − λ)3 . (a) Prove that it is impossible to find three linearly independent vectors vi , i = 1, 2, 3, such that Avi = vi , i = 1, 2, 3. ...
... 16. Suppose that A is a 6 × 6 matrix with characteristic polynomial cA (λ) = (1 + λ)(1 − λ)2 (2 − λ)3 . (a) Prove that it is impossible to find three linearly independent vectors vi , i = 1, 2, 3, such that Avi = vi , i = 1, 2, 3. ...
