Row Operation
Exercise Try different row operations on the augmented matrix in this
example. Then derive the same conclusion.
Exercise Solve systems of linear equations.
x_{1} 
 x_{2} 
+ 3x_{3} 
= 
3 
3x_{1} 
+ x_{2} 
+ x_{3} 
= 
5 
x_{1} 
+ x_{2} 
 x_{3} 
= 
1 
2x_{1} 
 3x_{2} 
 x_{3} 
= 
3 
x_{1} 
+ x_{2} 
+ 2x_{3} 
= 
1 
x_{1} 
+ 2x_{2} 
= 
3 
4x_{1} 
+ 5x_{2} 
= 
6 
7x_{1} 
+ 8x_{2} 
= 
9 
x_{1} 
+ 3x_{2} 
+ 2x_{3} 

+ x_{5} 
= 
0 
 x_{1} 
 x_{2} 
 x_{3} 
+ x_{4} 

= 
1 

4x_{2} 
+ 2x_{3} 
+ 4x_{4} 
+ 3x_{5} 
= 
3 
x_{1} 
+ 3x_{2} 
+ 2x_{3} 
 2x_{4} 

= 
0 
x_{1} 
+ 3x_{2} 
+ 2x_{3} 

+ x_{5} 
= 
0 
 x_{1} 
 x_{2} 
 x_{3} 
+ x_{4} 

= 
1 

4x_{2} 
+ 2x_{3} 
+ 4x_{4} 
+ 3x_{5} 
= 
2 
x_{1} 
+ 3x_{2} 
+ 2x_{3} 
 2x_{4} 

= 
0 
Answer
Exercise Prove that if a matrix A can be changed to a matrix
B by row operations, then the matrix B can also be changed to a matrix
A by row operations.
Answer