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Question 1043156: (1) Write the following sets of linear equation in augumented matrix form and solve for x1, x2, and x3 using Gauss Jordan Elimination method:
(a) 2X1 + X2 - X3 = 8
-3X1 - X2 + 2X3= -11
-2X1 + X2 + 2X3= -3
(b) 3X1 - X2 + 5X3 =-2
2X1 + 4X2 - X3 =3
-4X1 + X2 + 7X3 =10
(2) Using elementary row operations investigate the consistency of the following systems.
(a) 2X1 + 4X2 - 2X3 = 0
3X1 + 5X2 =1
(b) X1 - X2 + 2X3 =4
X1 + X3 = 6
2X1 - 3X2 + 5X3 =4
3X1 + 2X2 - X3 =1
(3) consider the system
X1 + 2X2 + 3X3 = a
2X1 + 5X2 + (a+5)X3 = -2+2a
- X2 + (a^2 - a)X3 = a^2 - a
find the values of a for which the system has
(a) No solution (b) exactly one solution (c) Infinitely many solutions.
thank you.
Answer by ikleyn(52794)   (Show Source):
You can put this solution on YOUR website! .
(1) Write the following sets of linear equation in augumented matrix form and solve for x1, x2, and x3 using Gauss Jordan Elimination method:
(a) 2X1 + X2 - X3 = 8
-3X1 - X2 + 2X3= -11
-2X1 + X2 + 2X3= -3
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Your matrix
№ X1 X2 X3 b
1 2 1 -1 8
2 -3 -1 2 -11
3 -2 1 2 3
Make the pivot in the 1st column by dividing the 1st row by 2
№ X1 X2 X3 b
1 1 1/2 -1/2 4
2 -3 -1 2 -11
3 -2 1 2 3
Eliminate the 1st column
№ X1 X2 X3 b
1 1 1/2 -1/2 4
2 0 1/2 1/2 1
3 0 2 1 11
Make the pivot in the 2nd column by dividing the 2nd row by 1/2
№ X1 X2 X3 b
1 1 1/2 -1/2 4
2 0 1 1 2
3 0 2 1 11
Eliminate the 2nd column
№ X1 X2 X3 b
1 1 0 -1 3
2 0 1 1 2
3 0 0 -1 7
Find the pivot in the 3rd column in the 3rd row (inversing the sign in the whole row)
№ X1 X2 X3 b
1 1 0 -1 3
2 0 1 1 2
3 0 0 1 -7
Eliminate the 3rd column
№ X1 X2 X3 b
1 1 0 0 -4
2 0 1 0 9
3 0 0 1 -7
Solution set:
x1 = -4
x2 = 9
x3 = -7
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