Question

We are working with rref matrices. what are the possible solutions to these matrices?

7. Describe all solutions to: [ 2 -2 [ 4 0 1 1 101 -9 21 | T = [2010] 14 i 21] [3] ſo 3 2 0 0] 3 3 2 2 ·ī=

Answer 1

what are the matries? possible salution to theise 12 0107 -2 1-9 14 1 21 [2 0 107 1:2 2 2 2 whe ran دم is [ 2o1o7 1-2 1-4 l.n 14 1 21 | . لما ی ented matrin is- (2 1-2 - 0 0 10 1-9 در تما : م 4 - 1 21 0 R = R2 tR, 2 G up rul - R}2 R₂ = 2R, - R3² Rg - R2 [20 10 ... ما لم O, Too 1 o . o.

Rank of coeffient marrin - Rank of Augmented matrin = 2 & The eqution are consistent or salveble. But Rank of coeffient makrin = ranky Augmited muth = 2 * numbers of unknown These matries has infinity mong salt Nove the system becomes - 2n, + long=2 - ant -5 - ③ from 9 let n=k then. [KE). kis an Infuger no. Fron (2) R₂ & k250 = N₂25-k & fron (1). 2n, tiong= 2 72, +10K = 2. > 2017 2-10K => n = 1-5k. u the solutions of malik is n,z 1-5k. ₂= 5-k. и; - и where K is an Integer non

T 2010 - 21-gã=o [4121] Augmented matrin is 2 o 10:17 7- 21 ago 14 1 21 31 R2 = R₂ + R, [2 o 10: 17 o i Rz? = R₂_2R l R, =R_R. 12 0 10 : 17 To. oool. Rank of coeffient Matrin = Rank of Augmented mahin=2 to Nos of unknown Thess system are consistent But has infinity mans salutions Non the system becons - 22, +100, z 1 - 0 ₂ + n 1 a.. ☺ Let nga m whe mis ang interfer no. cie me 2) .. Fro (1) 20,+lom = 1 2) 22, 2 1-10m 2 n 2 1-10m

From equin (3) n +1 21 in ₂t mal >) 1,21-m . The saletion of makin is n = 1-10m ₂ a 1-m ng -m wherer m EZ2 (m is an integn 10 ro 007 To7 [2 2 2 - Augmented matin is- Tooo: 3 3 3 : 12 122 28 R₂² R2 R3 To o o ó Tooool 2228] Rank of coeffient motrin Rank of Augmented Matrin = 1 & numbers of unknown .. These systen are consistent, but has intiner many salitions for The system becomes - 20,+212 +21₂ = 8 2) n. + ₂ + 2y = 4 . 0 Nove Let = p & M2 = 9 wle P 49. o are arbity interyrs le & P 9 € 2 in. 4

Feran I & From ear o ol Wit P+ q = 4. Miz 4-p-q These motrint They the salitions 1 i n i of mahrin is ,= 4-p-g n 2 2 q na a p wher p q EZ

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