CRAMMERS RULE

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Solving Systems of equations using Determinants : 

Solving Systems of equations using Determinants What are Determinants? Evaluating a 2x2 Determinant Expanding and Evaluating a 3x3 Determinant Using Cramer’s Rule to Solve a System of 2 Equations Using Cramer’s Rule to Solve a System of 3 Equations Gabriel Crammer

Why Study Determinants? : 

Why Study Determinants? Determinants offer a quick, number-crunching way to solve Systems of Equations No Graphing No Elimination Method No Substitution Method Put your equations in standard form Create a few determinants Evaluate them according to formulas

Concept:A Determinant is a Square Matrix : 

Concept:A Determinant is a Square Matrix # rows = # of columns Different Notations Matrix: Determinant:

Evaluating a 2x2 Determinant : 

Evaluating a 2x2 Determinant A 2x2 Determinant is always a number:It’s the Product of the main diagonal numbersminus the Product of the other diagonal numbers = ad – bc = 2(3) – 4(-1) = 10

Practice : 

Practice = ad – bc = 3(9) – 2(6) = 15 = -2(-4) – (-5)(-7) = -27 = 5(0) – ½(-1) = ½

Evaluating a 3x3 Determinant(expanding along the top row) : 

Evaluating a 3x3 Determinant(expanding along the top row) Expanding by Minors (little 2x2 determinants)

Array Signs for a 3x3 Determinant : 

Array Signs for a 3x3 Determinant You can expand across any row or down any column The Signs form a checkerboard pattern Use the Signs from this array

Expand Down the Middle Column : 

Expand Down the Middle Column Apply the Signs as you go down the column You always should get the same number

Using Cramer’s Rule to Solve a System of Two Equations : 

Using Cramer’s Rule to Solve a System of Two Equations

Applying Cramer’s Ruleon a System of Two Equations : 

Applying Cramer’s Ruleon a System of Two Equations

Class Exercise: Applying Cramer’s Ruleon a System of Two Equations : 

Class Exercise: Applying Cramer’s Ruleon a System of Two Equations

Using Cramer’s Rule to Solve a System of Three Equations : 

Using Cramer’s Rule to Solve a System of Three Equations

Applying Cramer’s Ruleon a System of Three Equations : 

Applying Cramer’s Ruleon a System of Three Equations

Class Exercise: Applying Cramer’s Ruleon a System of Three Equations : 

Class Exercise: Applying Cramer’s Ruleon a System of Three Equations

THANK YOU : 

THANK YOU

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