Systems of Linear Equations: Determinants

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Systems of Linear Equations: Determinants Section 11.3 Systems of Linear Equations: Determinants Copyright © 2013 Pearson Education, Inc. All rights reserved

Evaluate 2 by 2 determinants. Objectives Evaluate 2 by 2 determinants. Use Cramer’s Rule to solve a system of two equations containing two variables. Evaluate 3 by 3 determinants. Use Cramer’s Rule to solve a system of three equations containing three variables. Know the properties of determinants. Copyright © 2013 Pearson Education, Inc. All rights reserved

We are going to look at another method for solving systems of linear equations, but it only works when the number of equations equals the number of variables. Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Cramer’s Rule Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Inconsistent solutions and infinite solutions using Cramer’s Rule: If D=0 and at least one of Dx, Dy or Dz is NOT zero, the system is inconsistent and the solution set is Ø or { }. If D=0 and Dx = Dy = Dz = 0, the system is consistent and dependent so there are infinitely many solutions. The system must be solved using row reduction techniques. Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Properties of Determinants Copyright © 2013 Pearson Education, Inc. All rights reserved

Properties of Determinants Copyright © 2013 Pearson Education, Inc. All rights reserved

Properties of Determinants Copyright © 2013 Pearson Education, Inc. All rights reserved

Properties of Determinants Copyright © 2013 Pearson Education, Inc. All rights reserved

Homework 11.3 #7, 11, 15, 23, 27, 33, 37, 45, 59 Copyright © 2013 Pearson Education, Inc. All rights reserved