Cramer

1
Cramers Rule (4.3 Cont)(because Cramer RULES!)

• Gabriel Cramer was a Swiss mathematician
  (1704-1752)

2
Coefficient Matrices

• You can use determinants to solve a system of
  linear equations.
• You use the coefficient matrix of the linear
  system.
• Linear System Coeff Matrix axbye cxdyf

3
Cramers Rule for 2x2 System

• Let A be the coefficient matrix
• Linear System Coeff Matrix axbye cxdyf
  
• If detA 0, then the system has exactly one
  solution

and
4
Example 1- Cramers Rule 2x2

• Solve the system
• 8x5y2
• 2x-4y-10

The coefficient matrix is
and
So
and
5
Solution (-1,2)
6
Example 2- Cramers Rule 2x2

• Solve the system
• 2xy1
• 3x-2y-23

The solution is (-3,7) !!!
7
Example 3- Cramers Rule 3x3

• Solve the system
• x3y-z1
• -2x-6yz-3
• 3x5y-2z4

Lets solve for Z
Z1
The answer is (2,0,1)!!!
8
Assignment