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Finding the inverse of a matrix.

Finding the inverse of a matrix.

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  • 1. March 09, 20128.3 The Inverse of a Square MatrixObjective: Find and use the inverse matrix to solve systems of linear equations.Standard: Linear Algebra 9.0  1
  • 2. March 09, 2012Whats a MULTIPLICATIVE INVERSE?? 2
  • 3. March 09, 2012To be an inverse matrix: 3
  • 4. March 09, 2012Ex. 1﴿ Show that B is the Inverse of A. 4
  • 5. March 09, 2012Do all matrices have an inverse?Singular:Nonsingular ﴾aka: ________﴿ 5
  • 6. March 09, 2012Ex. 2﴿ Find the inverse of A if it exists.A= 6
  • 7. March 09, 2012The "Shortcut" for a 2x2 matrix If… and… ad – bc ≠ 0 then… 7
  • 8. March 09, 2012Ex. 2 Revisited﴿ Find the inverse of A if it exists.A= Ex. 3﴿ Find the inverse of A if it exists. 8
  • 9. March 09, 2012 9
  • 10. March 09, 2012Inverse of a 3x3 Matrix 10
  • 11. March 09, 2012Using Inverses for Systems of EquationsThe coefficient matrix… ` 11
  • 12. March 09, 2012Ex. 4﴿ Solve the systems using matrices. 12
  • 13. March 09, 2012Ex. 5﴿ Solve the system using matrices. 13
  • 14. March 09, 2012Assignment:8.3 p. 608 #4, 5, 11, 15, 17, 25, 27, 46, 49 14