2018年华南理工大学864高等代数考研真题.pdf

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864uHn2018ca )3K7LK8p;:, A, O, VnO, $21. (20) f(x), g(x)2Px, d(x) = (f(x);g(x) (f(x)d(x) 1,(g(x)d(x) 1, K3u(x);v(x)2Px u(x)f(x)+v(x)g(x) =d(x);p(u(x)(g(x)d(x);(v(x)(f(x)d(x).2. (20) On1:Dn =1 a1 a21 an 21 an 11 + Sa11 a2 a22 an 22 an 12 + Sa21 an a2n an 2n an 1n + San;pS =Qni=1ai.3. (20) A=0BBBBBB1 1 1 11 1 1 11 1 1 11 1 1 11CCCCCCA.(1) A 1;(2) eAB A=B, B0AB 1.11 4. (20) Am s, Bm n .(1) y AX =Bk)7r(A;B) =r(A);(2) XA=Bk)7o5. (20)AP5mV5C, f(x)2Pxf(A) =0, f(x) = f1(x)f2(x) fs(x) f1(x);f2(x);:;fs(x) p.-Vi = (fi(A) 1(0), i= 1;2;:;s. yV =V1 V2 Vs.6. (15) 5|8:x1 +x3 = 0;x2 +x4 = 0(1)mW, = (2;3;4;5)3WSK9 Wl.(5: d)V = V1 V?1 , ? 2Vk = 1 + 2, 1 2V1,22V?1 , 1 3fmV1SK.)7. (15)g.f(x1;x2;x3) = x21 +x22 +x23 4x1x2 4x1x3 +2ax2x3L5Ox=PyzIO.f = 3y21 +3y22 +by23,a;b9 P.8. (20) An n , kg, vAk = 0, y: An = 0.12
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