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研究所、轉學考(插大)◆邏輯
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107年 - 107 東吳大學_暑假轉學生招生考試_哲學系二年級：邏輯#105305
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題組內容
四、請用有效的推論規則證明下列論證（從前提推導出結論）
(2) /∴ (x)(P⊃P)
其他申論題
2. (x) Qx /∴ (x) Px
#446850
(2)1. (∃y) Ay /∴ (∃z) Az
#446851
1. P⊃Q
#446852
2. R⊃S /∴ (P∨R)⊃(Q∨S)
#446853
(3) 1. (∃x)( y) Lxy /∴ ( y) (∃x) Lxy
#446855
a. (5pts) Find the reduced row echelon form of its augmented matrix (A|b).
#446856
b. (10pts) Explicitly find the solution set K of this linear system, including a particular solution and a basis for its homogeneous solution set KH.
#446857
2. (15pts) Consider the following matrix Find a diagonal matrix D and an invertible matrix Q such that If it is impossible, give a convincing reason.
#446858
a. (5pts) Find the characteristic polynomial of T.
#446859
b. (5pts) Find the minimal polynomial m(x) of T. Explain why your answer is indeed minimal.Hint: by defnition, m(x) is the monic non-zero polynomial with smallest degree such that m(T) is the zero map onR4.
#446860
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