Solving Systems Use Gauss-Jordan reduction to transform
the augmented matrix of each system in Problems 24-36 to
RREF. Use it to discuss the solutions of the system (i.e., no
solutions, a unique solution, or infinitel y many solutions).
x+y=4
x-y=0
y=2x
y=x+3
x+y+z=0
y+z=1
2x+4y-2z=0
5x+3y=0
x-y-2z=1
2x+3y+z=2
5x+4y+2z=4
x_(1)+4x_(2)-5x_(3)=0
2x_(1)-x_(2)+8x_(3)=9
x+z=2
2x-3y+5z=4
3x+2y-z=4
x_(1)+x_(2)+2x_(3)=0
2x_(1)-x_(2)+x_(3)=0
4x_(1)+x_(2)+5x_(3)=0
x+2y+z=2
2x-4y-3z=0
-x+6y-4z=2
x-y=4
x-y+z=0
x+y=0
x+2y-z=0
x_(1)+x_(2)+2x_(3)=1
2x_(1)-x_(2)+x_(3)=2
4x_(1)+x_(2)+5x_(3)=4
x+2y+z=2
x-y=4
2x-y+2z=0
3y+z=-2
+2x_(3)-4x_(4)=1
x_(2)+x_(3)-3x_(4)=2
Using the Nonhomogeneous Principle Determine the solu-
tion set W for the associated homogeneous systems in Prob-
lems 37-49. Then write the solutions to the systems in the
original problems in the form vec(x)=vec(x)_(p)+vec(x)_(h), where vec(x)_(h)inW.
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Plz do 37-49 thanks
Pla
Solving Systems Use Gauss-Jordan reduction to transform the augmented matrix of each system in Problems 24-36 to RREF. Use it to discuss the solutions of the system (i.e., no solutions, a unique solution, or infinitely many solutions). 24. x + y = 4 25. y=2x x-y=0 y=x+3
26.x+y+z=0 y+z=1
27. 2x+4y-2z=0 5x + 3y =0
28.x - y - 2z = 1 2x+3y+z=2 5x +4y+2z= 4
29. x+4x2-5x3=0 2xi- x2+8x3=9
30.x +z=2 2x-3y+ 5z=4 3x+ 2y- z=4
31. x- y+z=0 x+ y=0 x+2y-z=0
32.x1 +x2 + 2x3=0 2x1-x2+x3=0 4xi+x2+5x3=0
33. xi+ x2+2x3=1 2x1-x2+x3=2 4xi + x2 +5x3=4
34. x+2y+z=2 2x-4y- 3z=0 -x +6y-4z=2 x- y =4
35. x+2y+z= 2 x- y = 4 2x-y+2z= 0 3y+ z=-2
36. xi +2x3-4x4=1 x2+x3-3x4=2
Using the Nonhomogeneous Principle Determine the solu- tion set W for the associated homogeneous systems in Prob- lems 37-49. Then write the solutions to the systems in the original problems in the form i = &p + xn. where x, e W.
37. Problem 24
38. Problem 25
39. Problem 26
40. Problem 27
41. Problem 28
42. Problem 29
43. Problem 30
44. Problem 31
45. Problem 32
46. Problem 33
47. Problem 34
48. Problem 35
49. Problem 36
