Class Work
Solving Systems of Linear Equations in Matrix Notation
Wednesday, Feb. 7, 2001
Math 1090-001 (Spring 2001)
Example
Solution
Solve

 x − 2y + 9z = 12
2x − y + 3z = 18

x + y − 6z = 6
Fill in the row operations that have been performed.


1 −2 9 12
 2 −1 3 18 
1 1 −6 6


1 −2
9 12
 0 3 −15 −6 
0 3 −15 −6


1 −2 9 12
 0 1 −5 −2 
0 0 0 0


1 0 −1 8
 0 1 −5 −2 
0 0 0 0
We can now read off that the system has infinitely many solutions as follows:
• Row 3 translates to 0 = 0, an identity. This indicates that the system has infinitely solutions.
• Row 1 translates to x = z + 8.
• Row 2 translates to y = 5z − 2.
Thus the complete solution to the system is:
(x, y, z) = (t + 8, 5t − 2, t),
t∈ .
1
Class Work
Solving Systems of Linear Equations in Matrix Notation
Wednesday, Feb. 7, 2001
Math 1090-001 (Spring 2001)
Example
Solution
Solve
2

 x − 4y + 3z = 4
2x − 2y + z = 6

x + 2y − 2z = 4
Fill in the row operations that have been performed.


1 −4 3 4
 2 −2 1 6 
1 2 −2 4


1 −4 3 4
 0 6 −5 −2 
0 6 −5 0


1 −4 3 4
 0 1 −5 −1 
6
3
0 0 0 2

8
1 0 − 13
3
 0 1 −5 −1 
6
3
0 0 0 1


1 0 − 13 0
 0 1 −5 0 
6
0 0 0 1

Now, Row 3 translates to
,
which means that the solution to the system
.