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Published byBasil Wright Modified over 6 years ago
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Applying Determinants to solve Systems of Equations 2x2 & 3x3
Cramer’s Rule Applying Determinants to solve Systems of Equations 2x2 & 3x3
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2x2 Determinants Det A = ad – cb
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Cramer’s Rule for 2x2 Part 1 1. Extract Coefficients
2. Calculate Determinant of Original Matrix
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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.
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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.
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Cramer’s Rule for 2x2 Part 4
To check x and y, substitute 51 in for x and 30 in for y.
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Ex #4 Solve
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3x3 Determinants
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Cramer’s Rule for 3x3 Part 1 Extract coefficients.
Calculate Original Determinant (OD) of Matrix
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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).
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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).
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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).
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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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