題組內容

109台大電信丙組
 9.(18%) Let
  627dc9beb4736.jpg
whose eigenvalues are -5, -2 and l.

(b) (6%) Please find the eigenvalues of 2A.

其他申論題

(c)  What is the determinant of this matrix?
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(d)  When will this matrix have its inverse? Please tell us your reason.
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(e)  Please evaluate (A - 2I)(A - 4I)(A - 51) + A, where I is a 3-by-3 identity matrix.
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(a) (6%) Plcase find the eigenvalues of.
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(c) (6%) Please find the eigenvalues of A2. 
#462093
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(AT-  λ l). By coming up with a 2 X 2 counter-example, show an example that the cigenvectors of A and ATneed not be the same.
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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.
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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. 
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