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研究所、轉學考(插大)◆線性代數
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110年 - 110東吳大學_碩士班招生考試_數學系︰線性代數#100057
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(b) Let E be an n × n elementary matrix, what is the determinant det(E) of E ?
其他申論題
12. (10 points) Let , x≥ 0. Use the mean value theorem for definite integral and the limit-definition of derivative to find f'(x). (Mean Value Theorem) Suppose f : [a,b] → IR is continuous on fa, b and differentiable on (a,b). Then there exists c (a,b) such that(Mean Value Theorem for Definite Integral) Suppose f : [a,b] → IR is a continuous function. Then there exists c [a,b] such that
#418916
1. (a) In R3, represent all the linear combinations of v=(2,0,1) and w=(0,1,2), give a geometric interpretation. And find a vector which is not a combination of v and w.
#418917
(b) In the following two planes, which one is a subspace of R3 (give your reasons) and find a basis for the subspace. x +2y-3z -4=0, 2x -4y +5z =0
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2. (a) If A is a 3 × 3 matrix has the determinant det(A) = -5, then what is det and det ?
#418919
(c) 8% For the matrix , find the value of , where is the cofactor of entry
#418921
3. For , find the reduced row echelon form of A and verify the dimension theorem for matrices.
#418922
4. Find the eigenvalues and eigenvectors of the matrix . Is A diagonalizable? And find the Jordan form of A.
#418923
5. Let R3 have the Euclidean inner product, and let v1 = (1, 0, 0), v2 = (1, 0, -1), v3 = (1,1, 0) . Use the Gram-Schmidt process to find the QR-decomposition of A =[ v1 v2 v3 ] .
#418924
1. 哈囉，寶貝。妳好嗎？妳今天都做了些什麼？妳有打電話給 Dr. Weber 先生嗎？他有 說什麼嗎？
#418925
2. 因為我沒辦法發簡訊或電子郵件，所以我會在路上尋找公用電話亭。不過我必須先 把所有電話號碼抄在一張紙條上，尤其是我女朋友的電話。
#418926
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