2017華南理工大學考研真題864_高等代數(shù)

1、864uHn?2017ca)?￡?3‰K’‰‰‰‰???7L?‰K’??￡‰8?p?“^’:A^O?V?nO$????2?1.(15?)?g(x)h(x)?P?‘?(g(x))=m?(h(x))=n…(g(x)h(x))=1.q?f(x)P???gnm?‘.y:?3r(x)s(x)∈P[x]?f(x)=r(x)g(x)s(x)h(x)r(x)=0?(r(x))n?(s(x))m.2.(20?)?n??g?5?|AX=b?X???r(A)

2、=1pA?n???X=(x1x2x3)?b=(b1b2b3)??=0.?η1η2η3AX=b?n?)?η1η2=(123)?η2η3=(0?11)?η3η1=(10?1)?T?|?:)X.3.(20?)?A?n???A?(ij)??aij=|i?j|1?|A|??.4.(20?)?α1α2α3n‘?mV??|…|???A=?????1?11?120104?????V??|IO??(^α1α2α3L5).11?5.(20?)?V?P?n‘

3、?5?mV1V?f?m…dimV1≥n2.(1)y:?3V?f?mW1W2?V=V1⊕W1=V1⊕W2?W1∩W2=0(2):?dimV1n2?(??o6.(20?)?f(x)g(x)?P?‘(f(x)g(x))=1AP?n???.y:f(A)g(A)=0?…=?r(f(A))r(g(A))=n.7.(20?)?AE?C???n???.(1)?λ1A???A??y:?3C?n??_??T?T?1AT=????????λ1b12b1n0b