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轉學考-線性代數
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94年 - 94 淡江大學 轉學考 線性代數#56042
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9. (10 points) Let P and Q be n x n matrices. We say P is similar to Q if there exists an invertible n x n matrix C such that C
-l
PC = Q. Prove that similar square matrices have the same eigenvalues with the same algebraic imilUplickies(代數重根數)•
其他申論題
(b) (5 points) Solve the linear system by Cramer’s rule.
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(a) (10 points) Find the characterisLic polynomial(特徵多項式),the real eigenvalues(特 徵值)> and the coriesponding eigenvectors(特徵向簠)of A.
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(b) (5 points) Find an invertible matrix C and a diagonal matrix(對角矩陣)D such that D 二 C-MC.
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【已刪除】8. (10 points) Let v1 and v2 be eigenvectors of a linear transformation T : V →V with corresponding eigenvalues λ1 and λ2 respectively. Prove that, and v2 are indepeudent(線性獨立).
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【已刪除】10. (10 points) Let A be an n x n matrix such that Ax • Ay = x • y for all vectors x and y in . Show that A is an orthogonal matrix(正交矩陣).
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(a) Sample mean
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(b) Sample median
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(c) Sample mode
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(d) Sample variance
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(e) Sample standard deviation
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