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Cramer’s Rule

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  1. Cramer’s Rule Applying Determinants to solve Systems of Equations 2x2 & 3x3

  2. 2x2 Determinants • Det A = ad – cb

  3. Cramer’s Rule for 2x2 • Part 1 • 1. Extract Coefficients • 2. Calculate Determinant of Original Matrix

  4. Cramer’s Rule for 2x2 • Part 2 (Solving for x) • Replace the 1st column of the coefficient matrix with the constant matrix. • Calculate the determinant of new matrix & divide by original determinant.

  5. Cramer’s Rule for 2x2 • Part 3 (Solving for y) • Replace the 2nd column of the coefficient matrix with the constant matrix. • Calculate the determinant of new matrix & divide by original determinant.

  6. Cramer’s Rule for 2x2 • Part 4 • To check x and y, substitute 51 in for x and 30 in for y.

  7. Ex #4 Solve

  8. 3x3 Determinants

  9. Cramer’s Rule for 3x3 • Part 1 • Extract coefficients. • Calculate Original Determinant (OD) of Matrix

  10. Cramer’s Rule for 3x3 • Part 2 (Solving for x) • Replace the 1st column of the coefficient matrix with the constant matrix. • Calculate the determinant of new matrix & divide by original determinant (15).

  11. Cramer’s Rule for 3x3 • Part 3 (Solving for y) • Replace the 2nd column of the coefficient matrix with the constant matrix. • Calculate the determinant of new matrix & divide by original determinant (15).

  12. Cramer’s Rule for 3x3 • Part 4 (Solving for z) • Replace the 3rd column of the coefficient matrix with the constant matrix. • Calculate the determinant of new matrix & divide by original determinant (15).

  13. Cramer’s Rule for 3x3 • Part 5 • 9. To check x and y, substitute 2.6 in for x, 2.2 in for y, and 0.2 in for z.

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