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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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題組內容
6. Given a linear system,
(a) (5 points) lYansfer this system as a matrix form Ax = b and write down A and b.
其他申論題
(a) (5 points) Find the standard matrix representation(標準矩陣表示式)of L.
#212624
(b) (5 points) Sliow that L is invertible(可逆）.
#212625
(c) (5 points) Find a formula for L-1
#212626
【已刪除】5. (10 points) Let K be a vector space with basis(基底）
#212627
(b) (5 points) Solve the linear system by Cramer’s rule.
#212629
(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.
#212630
(b) (5 points) Find an invertible matrix C and a diagonal matrix(對角矩陣）D such that D 二 C-MC.
#212631
【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).
#212632
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-lPC = Q. Prove that similar square matrices have the same eigenvalues with the same algebraic imilUplickies(代數重根數)•
#212633
【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).
#212634
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