# CRAMMERS RULE

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Category: Education

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## Presentation Transcript

### 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

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