Question

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

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)

Homework Answers

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

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