Question

Use Gaussian elimination to find the complete solution to the system of equations, or show that none exists. 5x +2y + 3z = -20 5x - 2y - 6z = -14 X+ y - z= 1 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. There is one solution. The solution set is {0 }. (Simplify your answers.) OB. There are infinitely many solutions. The solution set is {( z)}, where z is any real number (Type expressions using z as the variable. Use integers or fractions for any numbers in the expressions.) OC. There is no solution. The solution set is Ø.

Answer 1

P- Use Gaucian elimination to find the complete Solution to the system of equations or that none exists. 5x + 2y +32= -20 5x -y - 62 = -14 2 + y -z = 1 solution - The given system of Equations in the mateix form can be written as: r.207 -2 - 64 1 -14 - J Thus, the correspondung Augmented matuxur 552 3 :4207 $ -2 -6 : -14 L! 1 : 1 Apply Re- Rz-R,, we get :- 5 2 3 ; -207 0 -4 -9 6 Apply, R ZR, TI 45 315:47 10 -4 -9 . 6.

Apply Rz - Rz-R,, we get :- 215 315- -4 To -4 -9 . LO 315 -3/5 :5) Apply, Rz — trz, we get in Ti 35 3/5 ;-47 To LO 315 -81551 914 : 312 R, S R -2/5R2 R3 R3- 3/5 R2, 0 -3/10 . -1715-7 o 1 974 . -312 Loo 39/20: 59/10 | Apply, Rz - 20 R3, we get :- Tio -3/10 : 17157 914 : -312 Apply, we get :- 59 I 974 : 2 we get in Apply, Rg - R - Vulg. RI S R +3/10 R3 00-41 0 TO : 3 lo o I : -2

Thus, Again By compoung, we get :- =-4, 4= 3, 2= -09 Hence, (A) il correct solution. There is one solution. The solution is (-4, 3, -2) Ans.