Question

od the Inverse of eaich of the following matrices by two erent methods 1 2 3 B=402 A 14 5 620 أوجد الحل العام لنظام المعادلات الأكية باستخشام طريقة جاوس - جوردان - Solve cach of the following systems of equations using Gauss- Joindan method. )a+b+2c =8 i) 2x-y+3z-3 4x+2y-2z-2 6x-3y+z-9 a-2b+3c 1 3a-7b+4c 10

Answer 1

S Inverse of a matrix A using normal method re by A = Adi A here Adja = Adjoint of A T AL PAL- Determinant of A. Inverse existe only if 18+o Adjoint fA= (cofactor matris) - C7 where C=(Cofactor matrix) 3x3 (21 692 623 - for a given matrix [Gi (32 C33] A = [an 9,2 913. | a, a, a, [ 4,2 4,3 ban y ow column 1. 2017 Concs(23 S-41683-45) Second method (Gauss Jordan method) We form an angemented matrix with our given matrix Å and Identity matrix se [alI] => FACC)=1] -0 Then we apply Row operations, and " transform matrix A into Identity matsix. ac be some matrix. in Augemented on Augeme matrix

After low operations we get theal form. . ~[116] where [BA] > (1)©)=B] from equ0 and ③ we get C=A-! and c = B b1 First Method: Given A = [13] | 145 is if A= det A represented as I Al 1A) =-(1) (5) - 3(14) = -37 => A)= ad-bc - det A = ad-be costado () = CS 2 where c,= (t (s) = 5. (p=414 ; Cap =-3 ; 42=+1 % %7 [1437 437] .-37. ...A'Adja [ . IA) -37 Consider [A11] » [43]:] Second Method:

1рус» , , , , г. | | Appying , • Р. /., Appyrr, K, - к, - 38, -Г: Г.) - Гэмт В е 4 o о РФ 2 Т. First Method : 8?- AdiB 1в) : 1 (-1) - (--») +(-) 2 - 4 + 24 + 24 = 44 Cofactor matric of 8 be ca [ci C2 C37 | . с., . 3 LCз. с. <33

Cin = (-)*** | 28 | 21) (0-1) = 12 = (-1)'** 14 21 = -1) (2-0) = ? COLECOM 12: 1 - 61)(0-6). 6 922=611?21: :) - (1) (0-18) = -18 (3 = (-1)2+3 lei 1 -6)(2-12) = 10 (31 = (-1)}}|23|=()(4-0) = 4 Cazi (12+3 1421 = (-1) (2-12) = 10 C33 = 6-1)3+3 12.1 = 0) (0-8)= -8 (4 6 4. 6 -18 10 12-18 10 R P-1.1.5 17 (-262172 24 3 -4.5 2:5= 42-%2% 49 2 2.5 -2 412 5/22 -4/22 (A) Hence 8 = 1/2 % 2 % 2 ] | 22 - 9/22 5/22 14/12 9/22 -4/22

Second Methods Gauss Jordan Method болох der [в 11 4 о. Тог в 2 o Top Appeara R, - B, - 4 В., , R, - «R, | о -10 - - 6 от ?, ? *:/, - о -10 --6 от R, R, -2 В, , K, » , + 10 , Го и Точ, о

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