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無年度 - 主題課程_對角化:特徵值、特徵向量、特徵空間#107848
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109中興電機 (15 pts)
The eigenvalues of A and AT are the same, because det(A- λ l) -det(A- λ l)
T
= det(A
T
- λ l). By coming up with a 2 X 2 counter-example, show an example that the cigenvectors of A and A
T
need not be the same.
其他申論題
(e) Please evaluate (A - 2I)(A - 4I)(A - 51) + A, where I is a 3-by-3 identity matrix.
#462090
(a) (6%) Plcase find the eigenvalues of.
#462091
(b) (6%) Please find the eigenvalues of 2A.
#462092
(c) (6%) Please find the eigenvalues of A2.
#462093
106中興電機 (10pts) Suppose A is a real and symmetric matrix with order n, and has a repeated eigenvalue. Then for every i in {1,2, ... n}, there exists an eigenvector whose ith component is 0.
#462095
105中興電機 (10pts) Suppose A and B are two matrices with size m✕n and n✕m resbectively. Show that the nonzero eigenvalues of AB and BA are the same.
#462096
Let .Show that is linear combination of A and I2.
#462097
Suppose that T: R2→R3 is a linear transformation such that and Determine for any in R2.
#462098
Let T be a linear operator on R3 such that T, Please find the standard matrix of T.
#462099
(a) Find .
#462100