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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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(c) 8% For the matrix
, find the value of
, where
is the cofactor of entry
其他申論題
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.
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(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
#418918
2. (a) If A is a 3 × 3 matrix has the determinant det(A) = -5, then what is det and det ?
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(b) Let E be an n × n elementary matrix, what is the determinant det(E) of E ?
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3. For , find the reduced row echelon form of A and verify the dimension theorem for matrices.
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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 ] .
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3. 一位顧主有沒有吸引力，取決於員工的個人期待。眾多研究提出了下列幾個讓顧主 具有吸引力的因素。
#418927
, find the value of 
, where 
is the cofactor of entry
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, find the value of , where is the cofactor of entry