Question

Write the solution set of the given homogeneous system in parametric vector form. 2x1+2x2 + 4x3=0 4x1-4x2-8x3 =0 -6x2 + 6x3 = 0 where the solution set is x-X2 X3 (Type an integer or simplified fraction for each matrix element.)

Answer 1

Given Homogeneous system 2x_1 + 2 x_2 + 4 x_3 = 0_(1) - 4 x_1 - 4 x_2 - 8 x_3 = 0_(2) - 6 2 + 6 x_3 = 0_(3) Rightarrow - 6 x_2 = -6 x_3 x_2 = x_3 from equation (1) 2 x_1 + 2 x_2 + 4 x_2 = 0 2 x_1 + 6 x_2 = 0 1 = -3 x_2 let x_3 = k so, the solution of the given Homogeneous system in parametric vector form is Rightarrow x = [- 3 k k k] [Because x_2 = k or x_1 = -3 x_3 x_3 = k x_2 = x_3 x_1 = -3 k] x = k [- 3 1 1] or x = x_3 [- 3 1 1]