4.6 (A31, A32, A33); (A31, A32, 0)(a12,a11,0)(a22,a12,0). . , .

1. . .1. .2. ., . 4.6

4.6 1. 2. (1). . (3). .

4.6 3. . , , ki0, .

4.6 3. , , ().

4.6 3. , , , , |aij|, , A33, .

4.6 3. 1. (P.142, 4.22) x2+3xy-4y2+2x-10y=0. . . . . .. |aij|A33, , (4.42).. (4.42), (). , (4.42). .

4.6 2. (P.143, Ex. 5) . , (), . .(), (4.37),

4.6 3. , .. , (PQ, MN)=1., CM, CN.MPQClCMlPQ=NNCMClCNlCM=MCM, CN.

4.6 4. (P.144, Ex.9).. PA=BQ.ABM, , MN. CM, CN. MPQ, PA=BQ.

4.6 5. .. ABC.AB', A'B, lP. AB, A'B', t, t', 4.10, , (AB', A'B)(lAB, A'B'). .

4.6 6. (P.144, Ex.10), . . ACBM. M, P, Q. MPQ. 5, CPQ..5, . 36, , .

4.6 6. (P.144, Ex.11)PP'. QPR, P'QPRX. PR=RX. . PP', P, P'P. QP'T. PRT. 4.12, PT, P'R, PQU. , RUTP. RPX, PR=RX.P.

4.6 7. . P, Px, xP. xP(x). p.xPPlpCxp P 7. (P.143, Ex.7).

4.6 8. , TPQ, TPQN. TN. . , TNM. TN, TNM. TPQ, (TN, MM)= 1, MTN.

P.143, 4(1), 8The Class is over. Goodbye!