Question

(1) Use Euclid's algorithm to determine the HCF of 126 and 366. Give details of your working for each step. (2) Solve the following linear simultaneous equation using determinants (you must calculate Ao, A, and Ay): 2x + 3y = 20 x – 2y = -4 (3) Salvesta koying line (3) Solve the following linear simultaneous equation using determinants (you must calculate Ao, Ar, Ay and Ax): 2x + 3y – 4z = 17 x – y +z = -3 x + 2y – 2= 6

Answer 1

Answer 2

Nb 1261292 2 261 366 252 T14 Ans. HC.F (126, 83 66) fou ne we always divide greater number with smart number slep): Divide 366 by 126. We get a quotient and remaindy 114 so lhal- 366 = 126 X2 +14 Step2. Divide 126 by 114 we get I quotient and 12 remaindy so that 126 = 11441+ 12 . Step Divide 114 by 12 we get a quotient and 6 remaindus. 114 = 12x 9 + 6 x Stepy Divide 12 by 6: we get a quotient remaind o 70 hod na 6x2 to. As then no. remaundy .so devues 6 и HCP. i HCF = (126, 366) = 6. ve can check oul 126 2 X 3 X21 366 = 24361 2+3+3X7; 366=2+3861 common facts. 243/26 2x3x3x com

Ans. The mahih form of the system of linear squation ů AX=B. where Here det (A) = 0o = (-4-3)=-7 we can apply delerminant melhod we have: A = 120 3 1 -40+12=-28 -8- 20=-28 Ay=1379) = -5-202-28 we have x = AR = -28 = 4 Y = Ay = -28 = 4 : solutim set of lineer equation ů {x,y} = {4,4} 3) And The mality form of this system of ů Ax=3. When. knear squatum A-523-47 -) 1

A tere bo=det n = /2 3-4 2473-21:-)--21 . - 2 (1-2) - 3 (-1-1 -424)) = -2+6-12 = -1446=-8 : 40 =-8. determinant method xez AX Y = Dy Z 1 2 By 117 341 Ax=1-3 2 17-41 - 11-17(1-2) -3 (3-6) -4 (-676) = -17+9+0= -8 4-31 - 2 (3-6) - 17(-1-1) –4 (6+3) 1 =-6+34-36= 34-42=28 D2 = 1 2 2 11 ) = 2 (-6+6)-3 (6+3) + 17(2+1) =0-27+5)=24 لر ا ن IN solutum set of syslem of kiner Equation (x181Z) = (1, 11-3)