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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
4. Prove or disprove each of the following statements.
(c) det(A + D) =det(A)+dct(B), where clet(A) denotes the determinant of a square matrix A. (5%)
其他申論題
【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%)
#213554
【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%)
#213555
(a) Find the matrix representations of S、T and T o S relative to the standard basis. (6%)
#213557
(b) Find the matrix representations of S relative to the basis {(1，1)，(0, 2)}. (9%)
#213558
(c) Evaluate S100(1,—1). (10%)
#213559
(a) Find the characteristic polynomial and the minimal polynomial of A. ( 10%)
#213560
(b) Find the eigenvalues and the corresponding cigcnspaces of A. (10%)
#213561
(c) Find the Jodon canonical form J for A, and find a matrix P such that P-1 AP = J. (10%)
#213562
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