Gabriel Cramer was a Swiss mathematician ( )

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Presentation transcript:

Gabriel Cramer was a Swiss mathematician (1704-1752) Cramer’s Rule Gabriel Cramer was a Swiss mathematician (1704-1752)

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 ax+by=e cx+dy=f

Cramer’s Rule for 2x2 System Let A be the coefficient matrix Linear System Coeff Matrix ax+by=e cx+dy=f If detA 0, then the system has exactly one solution: and

Example 1- Cramer’s Rule 2x2 Solve the system: 8x+5y=2 2x-4y=-10 The coefficient matrix is: and So: and

Solution: (-1,2)

Example 2- Cramer’s Rule 2x2 Solve the system: 2x+y=1 3x-2y=-23 The solution is: (-3,7) !!!

Example 3- Cramer’s Rule 3x3 Solve the system: x+3y-z=1 -2x-6y+z=-3 3x+5y-2z=4 Let’s solve for Z Z=1 The answer is: (-2,0,1)!!!