Applying Determinants to solve Systems of Equations 2x2 & 3x3

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Presentation transcript:

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

2x2 Determinants Det A = ad – cb

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

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.

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.

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

Ex #4 Solve

3x3 Determinants

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

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).

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).

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).

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.