2016華南理工大學(xué)考研真題864_高等代數(shù)

1、864uHn?2016ca)?￡?3‰K’‰‰‰‰???7L?‰K’??￡‰8?p?“^’:A^O?V?nO$????2?1.(15?)?f(x)g(x)?P?g?u1?‘.y:(f(x)g(x))=1?…=??3???‘u(x)v(x)∈P[x]?u(x)f(x)v(x)g(x)=1p?(u(x))?(g(x))…?(v(x))?(f(x)).2.(15?)?f(x)=a1a2xanxn?1ε0ε1...εn?1???ng?y:D=a

2、1a2a3an?1anana1a2an?2an?1an?1ana1an?3an?2a3a4a5a1a2a2a3a4ana1=n?1?i=0f(εi).3.(20?)?A?n???vA2=A.y(1)r(A)r(A?E)=n(2)r(Ak)r(A?E)?=npk??g.4.(15?)??i=ci1x1ci2x2cinxni=12...pqpcij∈R.y￠?g.f(x1x2...xn)=?21?22?2p??2p1???2pq??.5?≤

3、pK.5?≤q.11?5.(15?)λ????e?|k)?k)???).?????????(3?2λ)x1(2?λ)x2x3=λ(2?λ)x1(2?λ)x2x3=1x1x2(2?λ)x3=1.6.(15?)??A=?????????2?1?10312001?1?13041????????A2016.7.(20?)?V=Rn[x]ef(x)=?ni=0aixig(x)=?ni=0bixi∈V5S(f(x)g(x))=?ni=0aibiKV

4、??m.W=f(x)∈V|f(1)=0.(1)yW?V?f?m‘??|IO??(2)W⊥??|IO??.8.(20?)?R2??5C?A3ε1=(12)ε2=(21)e?????1223???5C?B3η1=(11)η2=(12)e?????3324??.(1)AB3η1η2e??(2)AB3ε1ε2e??(3)?α=(33)Aα3ε1ε2e??I(4)Bα3η1η2e??I.9.(15?)?AB?n????v|A||B|=0.y:|A