1. Systems of Linear Equations: Determinants
Section 11.3
Systems of Linear Equations: Determinants
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2. 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.
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3. 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.
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8. Cramer’s Rule
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15. 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.
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18. Properties of Determinants
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19. Properties of Determinants
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20. Properties of Determinants
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21. Properties of Determinants
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22. Homework
11.3 #7, 11, 15, 23, 27, 33, 37, 45, 59
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