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Determinants of 2 x 2 and 3 x 3 Matrices

Determinants of 2 x 2 and 3 x 3 Matrices. By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org. Determinant of a 2 x 2 Matrix. d. b. a. c. -. Jeff Bivin -- LZHS. Example 1. Jeff Bivin -- LZHS. Determinant of a 2 x 2 Matrix. 3. 6. 4. 5. -. -2. =. Jeff Bivin -- LZHS.

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Determinants of 2 x 2 and 3 x 3 Matrices

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  1. Determinants of2 x 2 and 3 x 3Matrices By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org

  2. Determinant of a 2 x 2 Matrix d b a c - Jeff Bivin -- LZHS

  3. Example 1 Jeff Bivin -- LZHS

  4. Determinant of a 2 x 2 Matrix 3 6 4 5 - -2 = Jeff Bivin -- LZHS

  5. Example 2 Jeff Bivin -- LZHS

  6. Determinant of a 2 x 2 Matrix -4 2 5 3 - -23 = Jeff Bivin -- LZHS

  7. Example 3 Jeff Bivin -- LZHS

  8. Determinant of a 2 x 2 Matrix 8 5 6 4 - 16 = Jeff Bivin -- LZHS

  9. Example 4 Jeff Bivin -- LZHS

  10. Determinant of a 3 x 3 Matrix Jeff Bivin -- LZHS

  11. Determinant of a 3 x 3 Matrix Augment the determinant with the first two columns Jeff Bivin -- LZHS

  12. Determinant of a 3 x 3 Matrix Augment the determinant with the first two columns Jeff Bivin -- LZHS

  13. Determinant of a 3 x 3 Matrix Augment the determinant with the first two columns Jeff Bivin -- LZHS

  14. Determinant of a 3 x 3 Matrix Augment the determinant with the first two columns Jeff Bivin -- LZHS

  15. Determinant of a 3 x 3 Matrix Jeff Bivin -- LZHS

  16. Determinant of a 3 x 3 Matrix + + - - - Jeff Bivin -- LZHS

  17. Determinant of a 3 x 3 Matrix + + - - - Jeff Bivin -- LZHS

  18. Determinant of a 3 x 3 Matrix 1•1•7+ 3•5•3 + 4•2•6 - 3•1•4 - 6•5•1 - 7•2•3 Jeff Bivin -- LZHS

  19. Determinant of a 3 x 3 Matrix 1•1•7+ 3•5•3 + 4•2•6 - 3•1•4 - 6•5•1 - 7•2•3 Jeff Bivin -- LZHS

  20. Determinant of a 3 x 3 Matrix + 1•1•7 + 3•5•3+ 4•2•6 - 3•1•4 - 6•5•1 - 7•2•3 Jeff Bivin -- LZHS

  21. Determinant of a 3 x 3 Matrix + 1•1•7 + 3•5•3+ 4•2•6 - 3•1•4 - 6•5•1 - 7•2•3 Jeff Bivin -- LZHS

  22. Determinant of a 3 x 3 Matrix + + 1•1•7 + 3•5•3 + 4•2•6- 3•1•4 - 6•5•1 - 7•2•3 Jeff Bivin -- LZHS

  23. Determinant of a 3 x 3 Matrix + + 1•1•7 + 3•5•3 + 4•2•6- 3•1•4 - 6•5•1 - 7•2•3 Jeff Bivin -- LZHS

  24. Determinant of a 3 x 3 Matrix + + - 1•1•7 + 3•5•3 + 4•2•6 - 3•1•4- 6•5•1 - 7•2•3 Jeff Bivin -- LZHS

  25. Determinant of a 3 x 3 Matrix + + - 1•1•7 + 3•5•3 + 4•2•6 - 3•1•4- 6•5•1 - 7•2•3 Jeff Bivin -- LZHS

  26. Determinant of a 3 x 3 Matrix + + - - 1•1•7 + 3•5•3 + 4•2•6 - 3•1•4 - 6•5•1- 7•2•3 Jeff Bivin -- LZHS

  27. Determinant of a 3 x 3 Matrix + + - - 1•1•7 + 3•5•3 + 4•2•6 - 3•1•4 - 6•5•1- 7•2•3 Jeff Bivin -- LZHS

  28. Determinant of a 3 x 3 Matrix + + - - - 1•1•7 + 3•5•3 + 4•2•6 - 3•1•4 - 6•5•1 - 7•2•3 Jeff Bivin -- LZHS

  29. Determinant of a 3 x 3 Matrix + + - - - 1•1•7 + 3•5•3 + 4•2•6 - 3•1•4 - 6•5•1 - 7•2•3 Jeff Bivin -- LZHS

  30. Determinant of a 3 x 3 Matrix + + - - - 1•1•7 + 3•5•3 + 4•2•6 - 3•1•4 - 6•5•1 - 7•2•3 Jeff Bivin -- LZHS

  31. Determinant of a 3 x 3 Matrix + + - - - 1•1•7 + 3•5•3 + 4•2•6 - 3•1•4 - 6•5•1 - 7•2•3 Jeff Bivin -- LZHS

  32. Determinant of a 3 x 3 Matrix + + - - - 1•1•7 + 3•5•3 + 4•2•6 - 3•1•4 - 6•5•1 - 7•2•3 7 + 45 + 48 - 12 - 30 - 42 = 16 Jeff Bivin -- LZHS

  33. Example 5 Jeff Bivin -- LZHS

  34. Determinant of a 3 x 3 Matrix Augment the determinant with the first two columns Jeff Bivin -- LZHS

  35. Determinant of a 3 x 3 Matrix Augment the determinant with the first two columns Jeff Bivin -- LZHS

  36. Determinant of a 3 x 3 Matrix Augment the determinant with the first two columns Jeff Bivin -- LZHS

  37. Determinant of a 3 x 3 Matrix Augment the determinant with the first two columns Jeff Bivin -- LZHS

  38. Determinant of a 3 x 3 Matrix Augment the determinant with the first two columns Jeff Bivin -- LZHS

  39. Determinant of a 3 x 3 Matrix Augment the determinant with the first two columns Jeff Bivin -- LZHS

  40. Determinant of a 3 x 3 Matrix Augment the determinant with the first two columns Jeff Bivin -- LZHS

  41. Determinant of a 3 x 3 Matrix + + - - - Jeff Bivin -- LZHS

  42. Determinant of a 3 x 3 Matrix + + - - - Jeff Bivin -- LZHS

  43. Determinant of a 3 x 3 Matrix 1•1•7+ 3•5•3 + 4•2•6 - 3•1•4 - 6•5•1 - 7•2•3 Jeff Bivin -- LZHS

  44. Determinant of a 3 x 3 Matrix 2•3•8+ 1•7•5 + 6•4•9 - 5•3•6 - 9•7•2 - 8•4•1 Jeff Bivin -- LZHS

  45. Determinant of a 3 x 3 Matrix + 2•3•8 + 1•7•5 + 6•4•9 - 5•3•6 - 9•7•2 - 8•4•1 Jeff Bivin -- LZHS

  46. Determinant of a 3 x 3 Matrix + 2•3•8 + 1•7•5+ 6•4•9 - 5•3•6 - 9•7•2 - 8•4•1 Jeff Bivin -- LZHS

  47. Determinant of a 3 x 3 Matrix + + 2•3•8 + 1•7•5 + 6•4•9 - 5•3•6 - 9•7•2 - 8•4•1 Jeff Bivin -- LZHS

  48. Determinant of a 3 x 3 Matrix + + 2•3•8 + 1•7•5 + 6•4•9- 5•3•6 - 9•7•2 - 8•4•1 Jeff Bivin -- LZHS

  49. Determinant of a 3 x 3 Matrix + + - 2•3•8 + 1•7•5 + 6•4•9 - 5•3•6 - 9•7•2 - 8•4•1 Jeff Bivin -- LZHS

  50. Determinant of a 3 x 3 Matrix + + - 2•3•8 + 1•7•5 + 6•4•9 - 5•3•6- 9•7•2 - 8•4•1 Jeff Bivin -- LZHS

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