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96年 - 96 淡江大學 轉學考 代數#55974
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6. Prove that Z is a PID, where Z is the set of integers. (15%)
其他申論題
2. Show that a group G is abelian if for each g in G g2 = e, where e is the identity of G (15%)
#212215
3. Show that any group order 7 is cyclic. (15%)
#212216
4. Let G be a group such that 200 ＜ |G| ＜ 300. Suppose G has subgroups of order 21 and 33, find |G|. (15%)
#212217
【已刪除】5. Let R be a commutative ring with identity 1. Prove that an ideal P is a prime if and only if is an integral domain. (15%)
#212218
7. Up to isomorphism, find all abelian groups of order 12. (15%)
#212220
(a)y' +3y = 8 (20%)
#212221
(b)(2y-ey+6x2)y' +4 + 12xy =0 (20%) .
#212222
2. Show the differential equation is exact or not exact, if not exact find an integrating factor and general solution of different equation.(20%) 6xy+2y +8 + xy =0
#212223
【已刪除】3, Solve the initial value problem; (20%)
#212224
【已刪除】4. Find the eigenvalues of the matrix B and, for each eigenvalue, a corresponding eigenvector. Also check that eigenvectors associated with distinct eigenvalues are orthogonal, (20%)
#212225
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