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轉學考-線性代數
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89年 - 89 淡江大學 轉學考 線性代數#56164
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題組內容
1. Let M be the set consisting of m x n matrices with real entries.
(b) Give a basis for A4 and find the dimension of M, (5%)
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【已刪除】(a) Prove that is a vector space over . (5%)
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【已刪除】2. Let A be an n x n matrix with real entries. Let W be the null space of A, and let c be a particular solution to the system AX = B. Prove that c + W is the complete set of solutions to AX = B. (10%)
#213552
【已刪除】3. Let T : U→ V and S : V →W be linear transformations. Prove that the
#213553
【已刪除】 (a) If W and U are both subspaces of a vector space V, then is also a subspace of V. (5%)
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【已刪除】(b) If W and U are both subspaces of a vector space V y then is also a subspace of V (5%)
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(c) det(A + D) =det(A)+dct(B), where clet(A) denotes the determinant of a square matrix A. (5%)
#213556
(a) Find the matrix representations of S、T and T o S relative to the standard basis. (6%)
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