SOLUTION: (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

SOLUTION: (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

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(52797) (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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