2016华南理工大学考研真题864_高等代数.pdf
864uHnóÆ2016côÖa¬Æ ïÄ)ÆÁÁò£3Kþ§ÁòþçÁò7LKÓ£¤8¶¡µpê·µÄ:êÆ, AêÆ, OêÆ, VÇØênÚO, $ÊÆØ21. (15©) f(x)Úg(x)Ñ´êPþgêØu1õª.y²: (f(x);g(x) = 1 =3õªu(x);v(x) 2 Px ¦u(x)f(x) + v(x)g(x) = 1, ùp(u(x) >>>>:(3 2 )x1 + (2 )x2 + x3 = ;(2 )x1 + (2 )x2 + x3 = 1;x1 + x2 + (2 )x3 = 1:6. (15©) Ý A=0BBBBBB2 1 1 03 1 2 00 1 1 13 0 4 11CCCCCCA, ¦A2016.7. (20©) V = Rnx, ef(x) = Pni=0aixi, g(x) = Pni=0bixi 2V,5½SÈ(f(x);g(x) = Pni=0aibi, KVî¼m. -W =ff(x)2Vjf(1) = 0g:(1) y²WV fm, û½Ùê¿Þѧ|IOÄ(2) ÞÑW?|IOÄ.8. (20©) R2¥5CA3Ä“1 = (1;2), “2 = (2;1)eÝ0 1 22 31A, 5CB3Ä 1 = (1;1); 2 = (1;2)eÝ 0 3 32 41A.(1) ¦A +B3Ä 1; 2eÝ ;(2) ¦AB3Ä“1;“2eÝ ;(3) = (3;3), ¦A 3Ä“1;“2eI;(4) ¦B 3Ä 1; 2eI.9. (15©)A;BþnÝ , ÷vjAj+jBj= 0. y²: jA+Bj= 0.12