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MATRICES

Inverse & Identity. MATRICES. Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org. Last Updated: October 12, 2005. Inverses and Identities. 5x = 3. Jeff Bivin -- LZHS. Now with Matrices. ?. This is the Identity Matrix for 2 x 2 Matrices. Jeff Bivin -- LZHS.

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MATRICES

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  1. Inverse & Identity MATRICES Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org 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 Jeff Bivin -- LZHS

  4. Let’s look at another example Jeff Bivin -- LZHS

  5. New Question ? What do we multiply a matrix by to get the Identity? Jeff Bivin -- LZHS

  6. INVERSE The Inverse of a 2x2 Matrix Jeff Bivin -- LZHS

  7. INVERSE The Inverse of a 2x2 Matrix Jeff Bivin -- LZHS

  8. INVERSE The Inverse of a 2x2 Matrix Jeff Bivin -- LZHS

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

  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 Jeff Bivin -- LZHS

  15. INVERSE The Inverse of a 2x2 Matrix Jeff Bivin -- LZHS

  16. Does the Matrix have an Inverse? Find the determinant! Therefore,NOinverse! 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? + + Find the determinant! - - - 1•5•9 + 2•6•7 + 3•4•8 - 7•5•3 - 8•6•1 - 9•4•2 45 + 84 + 96 - 105 - 48 - 72 0 Therefore,NOinverse! Jeff Bivin -- LZHS

  19. Does the Matrix have an Inverse? + + Find the determinant! - - - 1•4•2 + 3•1•3 + 2•2•4 - 3•4•2 - 4•1•1 - 2•2•3 8 + 9 + 16 - 24 - 4 - 12 -7 Therefore, an inverse exists! Jeff Bivin -- LZHS

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

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

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