Question

Describe all solutions of Ax=0 in parametric vector form, where A is row equivalent to the given matrix. -2 -5 3 5-3 1 0 * +X integer or fraction for each matrix element.) (Type an

Answer 1

Ax = 0 where [1 0 - 2 1 - 5 5 3 - 3] is row equivalent to A Rightarrow solution of Ax = 0 will be same as. Solution of [1 0 - 2 1 - 5 5 3 - 3] [x_1 x_2 x_3 x_4] = 0, where x = [x_1 x_2 x_3 x_4] Rightarrow x_1 - 2x_2 - 5x_3 - 3x_4 = 0 and x_2 + 5x_3 + 3x_4 = 0 add both equation we get x_1 = x_2 so the solution system will be x = [x_1 x_2 x_3 x_4] = [x_1 x_2 x_3 x_4] Because x_1 = x_2 \r\n Rightarrow x = [x_1 x_2 x_3 x_4] = [- 5x_3 - 3x_4 - 5x_3 - 3x_4 x_3 x_4] Because x_2 + 5x_3 + 3x_4 = 0 Rightarrow x = x_3[- 5 - 5 1 0] + x_4[- 3 - 3 0 1] so the all solution of the system will be of following form. X = x_3[- 5 - 5 1 0] + x_4[- 3 - 3 0 1]