Augmented
Matrix
Exercise Find the augmented matrices.
2x_{1} 
 3x_{2} 
 x_{3} 
= 
3 
x_{1} 
+ x_{2} 
+ 2x_{3} 
= 
1 
x_{1} 
+ 2x_{2} 
+ 3x_{3} 
+ 4x_{4} 
= 
5 
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 
Answer
Exercise Recover systems of linear equations from the augmented matrices.
[ 
1 
0 
0 
0 
4 
] 
0 
1 
0 
0 
5 
0 
0 
1 
0 
6 
0 
0 
0 
1 
7 
[ 
0 
0 
0 
0 
0 
] 
0 
2 
0 
3 
4 
1 
1 
5 
0 
8 
Answer
Exercise The identity matrix I is
the square matrix with 1 on the diagonal and 0 off diagonal. For example, the
3 by 3 identity matrix is
I_{3} = [ 
1 
0 
0 
] 
0 
1 
0 
0 
0 
1 
Show that the system of equations corresponding to the augmented matrix [I_{n} b] is x = b.