logging in or signing up CRAMMERS RULE manpreet.oberoi2 Download Post to : URL : Related Presentations : Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Uploaded from authorPOINT lite Insert YouTube videos in PowerPont slides with aS Desktop Copy embed code: Embed: Flash iPad Dynamic Copy Does not support media & animations Automatically changes to Flash or non-Flash embed WordPress Embed Customize Embed URL: Copy Thumbnail: Copy The presentation is successfully added In Your Favorites. Views: 903 Category: Education License: All Rights Reserved Like it (0) Dislike it (0) Added: August 03, 2010 This Presentation is Public Favorites: 1 Presentation Description No description available. Comments Posting comment... Premium member 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 THANK YOU : THANK YOU You do not have the permission to view this presentation. In order to view it, please contact the author of the presentation.
CRAMMERS RULE manpreet.oberoi2 Download Post to : URL : Related Presentations : Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Uploaded from authorPOINT lite Insert YouTube videos in PowerPont slides with aS Desktop Copy embed code: Embed: Flash iPad Dynamic Copy Does not support media & animations Automatically changes to Flash or non-Flash embed WordPress Embed Customize Embed URL: Copy Thumbnail: Copy The presentation is successfully added In Your Favorites. Views: 903 Category: Education License: All Rights Reserved Like it (0) Dislike it (0) Added: August 03, 2010 This Presentation is Public Favorites: 1 Presentation Description No description available. Comments Posting comment... Premium member 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 THANK YOU : THANK YOU