8.6. Augmented Matrices http://www.ck12.org
3 x+y=− 15
x+ 2 y= 15- Use an augmented matrix to solve the following system.
−a+b−c= 0
2 a− 2 b− 3 c= 25
3 a− 4 b+ 3 c= 2Answers:
- The row reduction steps are not shown. Only the initial and final augmented matrices are shown.
2 1 1
0 2 6
1 1 0
∣∣
∣∣
∣∣
16
0
10
→
1 0 0
0 1 0
0 0 1
∣∣
∣∣
∣∣
7
3
− 1
2.
[3 1
1 2
∣∣
∣∣−^15
15
]
→
[1 0
0 1
∣∣
∣∣−^9
12
]
3.
− 1 1 − 1
2 − 2 − 3
3 − 4 3
∣∣
∣∣
∣∣
0
25
2
→
1 0 0
0 1 0
0 0 1
∣∣
∣∣
∣∣
3
− 2
− 5
Practice
Solve the following systems of equations using augmented matrices. If one solution does not exist, explain why not.
4 x− 2 y=− 20
x− 3 y=− 152.
3 x+ 5 y= 33
−x− 2 y=− 13x+ 4 y= 11
3 x+ 12 y= 33