Question

Convert the given linear system to an augmented matrix and then find all solutions. Write the solutions in parametric form.

2x₁ + 6x₂ − 9x₃ − 4x₄ = 0

−3x₁ − 11x₂ + 9x₃ − x₄ = 0

x₁ + 4x₂ − 2x₃ + x₄ = 0

Answer 1

2x2 + 6X₂ - 9x₂ - 4x4=0 - 2x - 11 x + 3x - X4 - 0 x & 4x2 - 2K3 traio we can write this the form ax=b system linear equation in where A-12 6-9-41 I be the 1-3 -22 g -1 matriny weffiunt of above equation now a and [A13 the ] be the augmented mattin of system, and A1B) = 12 6-9 -4 107 - 3119 ilol apply elementary in this case row operation A= on [Alb ] so the matrix we A. 126 -9-4lie 1-3-1 ä il Ž} 11 4 -2 1 [13-₂-2). 3R TI 3-621 1-3 -11 9 2 s10 -8-% -7 It a-2 t R3-R1 lot. 563

- RL [13 -96 blot la 2 R-3R2 3) А 5. 3 La - 2 ARB, o -4574 ot 914 -25 Rit A R2 | 1 R3 0 0 -35 7 72 Lo 0 1 -2 so the above system of equations equivalent equations are » -352=0, xr8x4 = 0,2. take neqat be any real number then 4= 35t, R₂ = -8t, &z=20 so the parametric Solution is (35t, 8t, zt, to where t be any real number,