students A and B were asked to solve the eigenvalues of the same matrix M
[a b c]
= [0 d 1]. Unfortunately, Student A mistook the value of d and obtained the
[0 2 e]
eigenvalues 0, 1, 3. Student B mistook the value of e and obtained the
eigenvalues 1, 1, -2.
(1) find the value of a 請問為什麼可以看出a=1?
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(2) If A is a 3*3 matrix with 3 distinct eigenvalues 0,1,2,
then the matrix (A+I) must be invertible
true 請問為什麼?
(3) An n*n matrix with n linearly independent eigenvectors is invertible
False 請問為什麼?
(4) If A is an n*n diagonalizable matrix, then each vector in R^n can be
written as a linear combination of eigenvectors of A
true 請問為什麼?
謝謝
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