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March 09, 2012



8.3 The Inverse of a 
Square Matrix
Objective: Find and use the inverse 
matrix to solve systems of linear 
equations.

Standard: Linear Algebra 9.0 




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March 09, 2012




What's a MULTIPLICATIVE 
INVERSE??




                                            2
March 09, 2012




To be an inverse matrix:




                                            3
March 09, 2012



Ex. 1﴿ Show that B is the Inverse of A.




                                                           4
March 09, 2012




Do all matrices have an inverse?


Singular:


Nonsingular ﴾aka: ________﴿




                                                    5
March 09, 2012



Ex. 2﴿ Find the inverse of A if it exists.

A=




                                                              6
March 09, 2012




The "Shortcut" for a 2x2 matrix
 If…          and…
                 ad – bc ≠ 0


  then…




                                                   7
March 09, 2012



Ex. 2 Revisited﴿ Find the inverse of A if 
it exists.

A=



 Ex. 3﴿ Find the inverse of A if it exists.




                                                               8
March 09, 2012




                 9
March 09, 2012



Inverse of a 3x3 Matrix




                                           10
March 09, 2012



Using Inverses for Systems 
of Equations



The coefficient matrix…




                          `




                                               11
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Ex. 4﴿ Solve the systems using matrices.




                                                            12
March 09, 2012



Ex. 5﴿ Solve the system using matrices.




                                                           13
March 09, 2012




Assignment:

8.3 p. 608 #4, 5, 11, 15, 17, 25, 
27, 46, 49




                                                      14

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