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Nhng iu cn ch khi lm bi tp

* | A | = 0 _ ma trn suy bin_ r(A) = r(A) < n (s vc t)_ ph thuc tuyn tnh

* | A | # 0 _ ma trn khng suy bin_ A kh nghch_ r(A) = r(A) = n_ h c nghim duy nht

* Vi h phng trnh tuyn tnh:

- s PT < s n => v s nghim r(A) = r( A )v nghim r(A) # r( A )

c nghim khng tm thng

- s PT = s n _ nu | A | = 0 => c nghim khng tm thng_ nu | A | # 0 => c nghim tm thng

A c ma trn nghch o khi A kh nghich c ngha l | A | # 0* Nu A l ma trn nghch o ca A th

nh thc ca A = nh thc ca A

VECT MA TRN H PHNG TRNH

TUYN TNHX + Y = Y + X(X + Y) + Z = X + (Y+Z)X + 0 = XX + (-X) = 01.X = X( + ).X = .X + .X(. )X = .( .X).(X+Y) = .X + .Y

(A . B).C= A.(B.C)A.(B+C) =A.B+A.Ck.(A.B)= k.A.BA.E =A, B.E =B ( E l matrn n v).Nu A, E l ma trnvung cng cp th A.E =E.A =A

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hng ca A = hng ca A

* Nu A l nh thc chuyn v ca A th | A | = | A|*Nu A v B l 2 ma trn vung cng cp th

=> | A.B | = | A | . | B |=> ( A.B )-1 = B -1 . A-1

* iu kin h phng trnh tuyn tnh c nghim l hng ca ma trncc h s = hng ca ma trn m rng

* i vi phng trnh tuyn tnh:- C nghim : khi | A | = | A|- C 1 nghim: khi | A | = | A| = s n- C v s nghim : khi | A | = | A| < s n

- C nghim tm thng : khi | A | # 0- C nghim khng tm thng: khi | A | = 0* i vi h phng trnh tuyn tnh thun nht

Nu s phng trnh = s n Phng trnh c nghim| A | # 0 tm thng

s pt = s n v | A | = 0N Nu r(A) = r(A) < s n Phng trnh c nghim

s pt < s n khng tm thng