H phng trnh tuyn tnh1, Cc khi nim c bn - Dng tng qut: a11x1 + a12x2 +...+ a1nxn = b1 a21x1+ a22x2 +...+ a2nxn = b2 .... am1x1+ am2x2+...+amnxn= bm gi l h phng trnh tuyn tnh: nu lp thnh ma trn th c m hng v n ct - Ta lp thnh ma trn sau: A = a11 a12 ... a1n a21 a22 ... a2n ... am1 am2 ... amn a11 a12 ... a1n b1 a21 a22 ... a2n b2 ... am1 am2 ... amn b3 gi l ma trn m rng ca h 2, Nghim v iu kin tn ti nghim - Mt vct n chiu X =( x1,x2,x3,...,xn) c gi l ngim khi thay n vo h th thy tho mn mi phng trnh. - iu kin cn v h c nghim l hng ca ma trn cc h s = hng ca ma trn m rng.=> nu A v A c chung nh thc con cp cao nht # 0 th r(A) = r(A) 3, Cch gii phng trnh tuyn tnh * Phng php kh dn cc n - 3 php bin i s cp : i ch 2 phng trnh Nhn 2 v ca phng trnh vi cng 1 s # 0 Nhn 2 v ca phng trnh vi 1 s bt k ri cng vo hai v tng ng ca phng trnh khc. A=

=> cc php bin i s cp khng lm thay i nghim ca h phng trnh. * Phng php Cramer - nh ngha: Mt h c n phng trnh tuyn tnh, n n vi nh thc ca ma trn h s # 0 c gi l Cramer - iu kin l |A| # 0 => r(A) = r( A ) => C nghim duy nht. - CH : Cch ny ch dng cho h vung vi h s ma trn khng suy bin ( |A| # 0) * Phng php nghch o X.A = B X.A.A-1 = B.A-1 X = B.A-1 * H phng trnh vi ma trn h s c dng hnh thang sau khi bin i s cp h a v dng: a11.x1 + a12.x2 + ...+ a1r.xr +...+ a1n.xn = 1 a22.x2 + ...+ a2r.xr +...+ a2n.xn = 2 (3.3) .... arr.xr +...+ arn.xn = r Ta phi chn c n c s ri biu din cc n t do qua cc n c s.Cho mi n t do 1 gi tr nht nh ta s c 1 nghim ring. Nh vy h (3.3) c v s nghim ring. 3, H phng trnh thun nht * Dng tng qut: a11x1 + a12x2 +...+ a1nxn = 0 a21x1+ a22x2 +...+ a2nxn = 0 .... am1x1+ am2x2+...+amnxn= 0 do ct cui ca A = 0 nn r(A) = r( A ) => Phng trnh lun c nghim * i vi h phng trnh tuyn tnh thun nht

Nu

s phng trnh = s n |A| #0

Phng trnh c nghim tm thng

N Nu

s pt = s n v | A | = 0 r(A) = r(A) < s n s pt < s n

Phng trnh c nghim khng tm thng