M 1313
Popper 06 and PS# (must bubble)
On purple scantron you need to bubble A for questions 1-5.
1. Given the following system of equations, solve using the GaussJordan Elimination Process.
5 
1 − 1 2


0 5 − 5 − 5 
0 − 1 − 6 − 20
2. Perform the operation:
4
 3 1 2  

 1 
− 1 2 4  
− 2
3. Solve using matrix equations:
4 x + y = −7
− 5 x − y = 10
Soutions:
1. Given the following system of equations, solve using the GaussJordan Elimination Process.
5 
1 − 1 2
1
0 5

− 5 − 5  R2 • → R 2

5
0 − 1 − 6 − 20 
5 
1 − 1 2
0 1
 R2 + R1 → R1
−1 −1 

R + R3 → R3
0 − 1 − 6 − 20  2
4 
1 0 1
1
0 1

− 1 − 1  R3 • − → R3

7
0 0 − 7 − 21
4
1 0 1
0 1
 − R 3 + R1 → R 1
1
1
−
−

 R +R →R
2
2
0 0 1
3  3
1 0 0 1 


0 1 0 2 
0 0 1 3
x=1, y=2, y=3
2. Perform the operation:
4
 3 1 2  

 1 
− 1 2 4  
− 2
3. Solve using matrix equations:
4 x + y = −7
− 5 x − y = 10