1. Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org
Inverse & Identity
MATRICES
Jeffrey Bivin
Lake Zurich High School
Last Updated: October 12, 2005

2. Inverses and Identities
5x = 3
Jeff Bivin -- LZHS

3. Now with Matrices ? This is the Identity Matrix for 2 x 2 Matrices
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4. Let’s look at another example
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5. What do we multiply a matrix by to get the Identity?
New Question ?
What do we multiply a matrix by to get the Identity?
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6. The Inverse of a 2x2 Matrix
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7. The Inverse of a 2x2 Matrix
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8. The Inverse of a 2x2 Matrix
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9. A B
This is our Formula!
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10. A B
This is our Formula!
Jeff Bivin -- LZHS

11. A B C
This is our Formula!
Jeff Bivin -- LZHS

12. Are the two Matrices Inverses?
The product of inverse matrices is the identity matrix.
Identity, therefore, INVERSE
Matrices
Jeff Bivin -- LZHS

13. Are the two Matrices Inverses?
The product of inverse matrices is the identity matrix.
Not the Identity, therefore, NOT INVERSE
Matrices
Jeff Bivin -- LZHS

14. Does the Matrix have an Inverse?
Let’s review the definition of the Inverse of a 2x2 Matrix
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15. The Inverse of a 2x2 Matrix
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16. Does the Matrix have an Inverse?
Find the determinant!
Therefore, NO inverse!
Jeff Bivin -- LZHS

17. Does the Matrix have an Inverse?
Find the determinant!
Therefore, an inverse exists!
Jeff Bivin -- LZHS

18. Does the Matrix have an Inverse?+ + 1 2 3 4 5 6 7 8 9
Find the determinant! - - -
1•5•9 + 2•6•7 + 3•4•8 - 7•5•3 - 8•6•1 - 9•4•2
Therefore, NO inverse!
Jeff Bivin -- LZHS

19. Does the Matrix have an Inverse?+ + 1 3 2 4
Find the determinant! - - -
1•4•2 + 3•1•3 + 2•2•4 - 3•4•2 - 4•1•1 - 2•2•3 -7
Therefore, an inverse exists!
Jeff Bivin -- LZHS

20. Solve the system using inverse matricesB
3x + 2y = 7
4x - 5y = 11
This is our Formula!
Jeff Bivin -- LZHS

21. Solve the system using inverse matricesB
2x - 4y = 9
3x - 2y = 1
This is our Formula!
Jeff Bivin -- LZHS