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研究所、轉學考(插大)◆工程數學
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108年 - 108 國立臺灣大學_碩士班招生考試：工程數學(D)#124907
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題組內容
2. Let the matrix A =
. Then
(a) (6%) Find all the eigenvalues of A.
其他申論題
(g) Let A and B be n x n matrices. If A is similar to B, then A and B have the same eigenvalues.
#531187
(h) If the vectors v1, v2, and v3 are linearly independent, then the fol- lowing vectors 2v1 + v2 + 2v3, v2 + v3, v2 + 2v3 are also linearly independent.
#531188
(i) Let v1 and v2 be n x 1 vectors. Then rank() = 2.
#531189
(j) Let A be an n x n symmetric matrix. Let v be an n x 1 vector. If Av = 0, then Av = 0.
#531190
(b) (6%) Find an orthonormal basis for R3, consisting of the eigenvectors of A.
#531192
(c) (6%) Find , where e1 = .
#531193
(d) (2%) Find the nullity of A.
#531194
(a) (4%) Find T.
#531195
(b) (6%) Find T
#531196
(a) What is the mathematical definition of a RV? (3%)
#531197
. Then
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. Then