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Determinants of 2 x 2 and 3 x 3 Matrices

Learn about the determinants of 2x2 and 3x3 matrices with examples and augmentation techniques.

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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

  2. Determinant of a 2 x 2 Matrix d b a c -

  3. Example 1

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

  5. Example 2

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

  7. Example 3

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

  9. Example 4

  10. Determinant of a 3 x 3 Matrix

  11. Determinant of a 3 x 3 Matrix Augment the determinant with the first two columns

  12. Determinant of a 3 x 3 Matrix Augment the determinant with the first two columns

  13. Determinant of a 3 x 3 Matrix Augment the determinant with the first two columns

  14. Determinant of a 3 x 3 Matrix Augment the determinant with the first two columns

  15. Determinant of a 3 x 3 Matrix

  16. Determinant of a 3 x 3 Matrix + + - - -

  17. Determinant of a 3 x 3 Matrix + + - - -

  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

  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

  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

  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

  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

  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

  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

  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

  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

  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

  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

  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

  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

  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

  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

  33. Example 5

  34. Determinant of a 3 x 3 Matrix Augment the determinant with the first two columns

  35. Determinant of a 3 x 3 Matrix Augment the determinant with the first two columns

  36. Determinant of a 3 x 3 Matrix Augment the determinant with the first two columns

  37. Determinant of a 3 x 3 Matrix Augment the determinant with the first two columns

  38. Determinant of a 3 x 3 Matrix Augment the determinant with the first two columns

  39. Determinant of a 3 x 3 Matrix Augment the determinant with the first two columns

  40. Determinant of a 3 x 3 Matrix + + - - -

  41. Determinant of a 3 x 3 Matrix + + - - -

  42. 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

  43. 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

  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

  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

  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

  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

  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

  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

  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

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