Question

Solve the system. If there's no unique solution, label the system as either dependent or incomsistent.

2x+y+3z=12

x-y+4z=5

-4x+4y-4z=-20

a. Dependent system

b. inconsistent system

c.(1,4,2)

d. (4,1,2)

Answer 1

system is

augmented matrix is

2	1	3	12
1	-1	4	5
-4	4	-4	-20

convert into Reduced Row Eschelon Form...

Divide row1 by 2

1	1/2	3/2	6
1	-1	4	5
-4	4	-4	-20

Add (-1 * row1) to row2

1	1/2	3/2	6
0	-3/2	5/2	-1
-4	4	-4	-20

Add (4 * row1) to row3

1	1/2	3/2	6
0	-3/2	5/2	-1
0	6	2	4

Divide row2 by -3/2

1	1/2	3/2	6
0	1	-5/3	2/3
0	6	2	4

Add (-6 * row2) to row3

1	1/2	3/2	6
0	1	-5/3	2/3
0	0	12	0

Divide row3 by 12

1	1/2	3/2	6
0	1	-5/3	2/3
0	0	1	0

Add (5/3 * row3) to row2

1	1/2	3/2	6
0	1	0	2/3
0	0	1	0

Add (-3/2 * row3) to row1

1	1/2	0	6
0	1	0	2/3
0	0	1	0

Add (-1/2 * row2) to row1

1	0	0	17/3
0	1	0	2/3
0	0	1	0

reduced system is

solution is