Question

5. Use Gauss' Method to find the general solution of the system and give one particular solution. [6x, + 3x₂ + 2x₂ + 3x₂ + 4x, = 3 4x, +2x2 + x3 + 2x4 +3x, = 2. 1 2x + x₂ + x₃ + x₂ + x = 7

Answer 1

given sistem of equcetion is 621+ sea +222 +32 4+4x5 =3 481 +222 +22 +224 +325 = 62 21+ 2zt azt antxy = 7 in to EoAs we write this system of equation meetrix form Ax=b where A=16 3 2 347 A XXXNX considen [A167 Augmented matrix 6 3 2 3 4 13 4 2 2 3 2 we solve this by gauss elimination method performing operation Retri Il/a 7 £ & 1 £ 7 4 2 2 32 La II 1171 Now performing R₂ to R₂-4 R18 R₂ R3-2 R1 I - 3 1 Ł] wt what wt lo o Ž 0 3 16 x, + 1 2 2 2 + z g + t Rutt 25 = - 123+55 : 0 I x3 + $# -o - * - @ 3

Here n=5 (number of variable f Me 3 (number of equation) i n -m= 9-3 = 2 2 Nanubie are free in X2= t and 2n=5] ster we solving to Í X3+ & X5 - 0 & + 3+ tas = 6 Bultiply both the equations by 3 -x3 + 5x5=0 S x3 +25= 18 adding them = 5x5=18 - 25=3 from this x3 = 5(89) = 5(3) = 15 23=15 from x = 1 - 2 - 3 / x4 + 1/ 325 - - £t - 13 (15) - - 5 - 33 (3) = - + - 5 - Łs-1 =-11 - 2 - 3 212 Ž [11+++5]

Genre solution of the system is (21, ne, dz, k4, 85)= (-1/3 ( 11ttts), t, 15, 5,3), suteir we find perticular solution take s=t=0 2) (x1, xr, ds, 24, 25) = (-12, 0, 15, 0,3)