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Cramer’s Rule for 2x2 systems

Jerry, I'm at the corner of 1st and 1st. Wait a minute, how can a street intersect itself? I must be at the nexus of the universe!. Cramer’s Rule for 2x2 systems. Cramer’s Rule. Actually, Gabriel Cramer was a Swiss mathematician (1704 -1752). Coefficient Matrices.

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Cramer’s Rule for 2x2 systems

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  1. Jerry, I'm at the corner of 1st and 1st. Wait a minute, how can a street intersect itself? I must be at the nexus of the universe! Cramer’s Rule for 2x2 systems

  2. Cramer’s Rule Actually, Gabriel Cramer was a Swiss mathematician (1704 -1752)

  3. 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

  4. 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

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

  6. Solution: (-1,2)

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

  8. Example 3- Cramer’s Rule 2x2 • Solve the system: • 5x+2y=8 • 2x-3y= 7 The solution is: (2,-1) !!!

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