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Cramer’s Rule

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.

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Cramer’s Rule

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  1. Cramer’s Rule 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 SystemCoeff Matrix ax+by=e cx+dy=f

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

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

  5. Solution: (-1,2)

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

  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)!!!

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