1. 3 X 3 DETERMINANTS
DIAGONALS METHOD

2. DIAGONALS METHOD
COPY 1ST TWO COLUMNS

3. DIAGONALS METHOD
COPY 1ST TWO COLUMNS 5 -1 3

4. DIAGONALS METHOD
COPY 1ST TWO COLUMNS
5 2
-1 4
3 0

5. DIAGONALS METHOD
MULTIPY DOWN !!
5 2
-1 4
3 0

6. DIAGONALS METHOD
MULTIPY DOWN !!
5 2
-1 4
3 0

7. DIAGONALS METHOD
MULTIPY DOWN !!
5 2
-1 4
3 0
120

8. DIAGONALS METHOD
MULTIPY DOWN !!
5 2
-1 4
3 0
120

9. DIAGONALS METHOD
MULTIPY DOWN!!
5 2
-1 4
3 0
120 +0

10. DIAGONALS METHOD MULTIPY DOWN !! 5 2 7 -1 4 0 3 0 6 5 2 -1 4 3 0 120
5 2
-1 4
3 0
120 +0

11. DIAGONALS METHOD MULTIPY DOWN !! 5 2 7 -1 4 0 3 0 6 5 2 -1 4 3 0 120
5 2
-1 4
3 0
120 +0 0+

12. DIAGONALS METHOD MULTIPY DOWN!! 5 2 7 -1 4 0 3 0 6 5 2 -1 4 3 0 120 +0
5 2
-1 4
3 0
120 +0 0+ =

13. DIAGONALS METHOD MULTIPY DOWN !! 5 2 7 -1 4 0 3 0 6 5 2 -1 4 3 0 120
5 2
-1 4
3 0
120 +0 0+
= 120

14. DIAGONALS METHOD
5 2
-1 4
3 0
DOWN = 120

15. DIAGONALS METHOD MULTIPLY UP !! 5 2 7 -1 4 0 3 0 6 5 2 -1 4 3 0
5 2
-1 4
3 0
DOWN = 120

16. DIAGONALS METHOD MULTIPLY UP !! 5 2 7 -1 4 0 3 0 6 5 2 -1 4 3 0
5 2
-1 4
3 0
DOWN = 120

17. DIAGONALS METHOD MULTIPLY UP !! 5 2 7 5 2 84 -1 4 0 -1 4 3 0 6 3 0
5 2
-1 4
3 0 84
DOWN = 120

18. DIAGONALS METHOD MULTIPLY UP !! 5 2 7 -1 4 0 3 0 6 5 2 -1 4 3 0 84
5 2
-1 4
3 0 84
DOWN = 120

19. DIAGONALS METHOD MULTIPLY UP !! 5 2 7 5 2 84 + 0 -1 4 0 -1 4 3 0 6 3 0
5 2
-1 4
3 0
84 + 0
DOWN = 120

20. DIAGONALS METHOD MULTIPLY UP !! 5 2 7 5 2 84 + 0 -1 4 0 -1 4 3 0 6 3 0
5 2
-1 4
3 0
84 + 0
DOWN = 120

21. DIAGONALS METHOD MULTIPLY UP !! 5 2 7 -1 4 0 3 0 6 5 2 -1 4 3 0
5 2
-1 4
3 0
(-12)
DOWN = 120

22. DIAGONALS METHOD MULTIPLY UP !! 5 2 7 -1 4 0 3 0 6 5 2 -1 4 3 0
5 2
-1 4
3 0
(-12) =
DOWN = 120

23. DIAGONALS METHOD MULTIPLY UP !! 5 2 7 -1 4 0 3 0 6 5 2 -1 4 3 0
5 2
-1 4
3 0
(-12)
= 72
DOWN = 120

24. DIAGONALS METHOD MULTIPLY UP !! 5 2 7 -1 4 0 3 0 6 5 2 -1 4 3 0
5 2
-1 4
3 0
(-12)
= 72
DOWN = 120

25. DIAGONALS METHOD MULTIPLY UP !! 5 2 7 5 2 84 + 0 + (-12) -1 4 0 -1 4
5 2
-1 4
3 0
(-12)
= 72
ALWAYS: DOWN-UP
DOWN = 120

26. DIAGONALS METHOD MULTIPLY UP !! 5 2 7 -1 4 0 3 0 6 5 2 -1 4 3 0
5 2
-1 4
3 0
(-12)
= 72
ALWAYS: DOWN-UP
DOWN = 120
120 -

27. DIAGONALS METHOD MULTIPLY UP !! 5 2 7 -1 4 0 3 0 6 5 2 -1 4 3 0
5 2
-1 4
3 0
(-12)
= 72
ALWAYS: DOWN-UP
DOWN = 120
120 - 72

28. DIAGONALS METHOD MULTIPLY UP !! 5 2 7 -1 4 0 3 0 6 5 2 -1 4 3 0
5 2
-1 4
3 0
(-12)
= 72
ALWAYS: DOWN-UP
DOWN = 120
120 -
72 =

29. DIAGONALS METHOD MULTIPLY UP !! 5 2 7 -1 4 0 3 0 6 5 2 -1 4 3 0
5 2
-1 4
3 0
(-12)
= 72
ALWAYS: DOWN-UP
DOWN = 120
120 -
72 = 48

30. 3 X 3 DETERMINANTS
EXPANSION BY MINORS METHOD

31. 3 X 3 DETERMINANTS FINDING A MINOR 5 2 7 -1 4 0 3 0 6
EXAMPLE 1: THE MINOR
OF ELEMENT ‘5’:
ROW 1,COLUMN 1

32. FINDING A MINOR 5 2 7 CROSS OUT ROW AND COLUMN CONTAINING ‘5’ -1 4 0
EXAMPLE 1: THE MINOR OF
ELEMENT ‘5’:ROW 1,COLUMN 1
CROSS OUT ROW AND COLUMN CONTAINING ‘5’

33. FINDING A MINOR CROSS OUT ROW AND COLUMN CONTAINING ‘5’ 5 2 7 -1 4 0
EXAMPLE 1: THE MINOR OF ELEMENT ‘5’:ROW 1,COLUMN 1
CROSS OUT ROW AND COLUMN CONTAINING ‘5’

34. FINDING A MINOR 5 2 7 CROSS OUT ROW AND COLUMN CONTAINING ‘5’ -1 4 0
EXAMPLE 1: THE MINOR OF ELEMENT ‘5’:ROW 1,COLUMN 1
CROSS OUT ROW AND COLUMN CONTAINING ‘5’

35. FINDING A MINOR
EXAMPLE 1: THE MINOR OF ELEMENT ‘5’:ROW 1,COLUMN 1
THE REMAINING ELEMENTS ARE CALLED THE MINOR MATRIX

36. FINDING A MINOR THE REMAINING ELEMENTS ARE CALLED THE MINOR 5 2 7
EXAMPLE 1: THE MINOR OF
ELEMENT ‘5’:ROW 1,COLUMN 1
THE REMAINING ELEMENTS ARE CALLED THE MINOR
MATRIX =>
4 0
0 6

37. FINDING A MINOR EXAMPLE 2: THE MINOR OF ELEMENT ‘2’:ROW 1,COLUMN 2

38. FINDING A MINOR EXAMPLE 2: THE MINOR OF ELEMENT ‘2’:ROW 1,COLUMN 2
CROSS OUT ROW AND COLUMN CONTAINING ‘2’

39. FINDING A MINOR EXAMPLE 2: THE MINOR OF ELEMENT ‘2’:ROW 1,COLUMN 2
CROSS OUT ROW AND COLUMN CONTAINING ‘2’

40. FINDING A MINOR EXAMPLE 2: THE MINOR OF ELEMENT ‘2’:ROW 1,COLUMN 2
CROSS OUT ROW AND COLUMN CONTAINING ‘2’

41. FINDING A MINOR EXAMPLE 2: THE MINOR OF ELEMENT ‘2’:ROW 1,COLUMN 2
THE REMAINING ELEMENTS
ARE CALLED THE MINOR
MATRIX =>
-1 0
3 6

42. FINDING A MINOR EXAMPLE 3: THE MINOR OF ELEMENT ‘7’:ROW 1,COLUMN 3
CROSS OUT ROW AND COLUMN CONTAINING ‘7’

43. FINDING A MINOR EXAMPLE 3: THE MINOR OF ELEMENT ‘7’:ROW 1,COLUMN 3
CROSS OUT ROW AND COLUMN CONTAINING ‘7’

44. FINDING A MINOR EXAMPLE 3: THE MINOR OF ELEMENT ‘7’:ROW 1,COLUMN 3
CROSS OUT ROW AND COLUMN CONTAINING ‘7’

45. FINDING A MINOR EXAMPLE 3: THE MINOR OF ELEMENT ‘7’:ROW 1,COLUMN 3
THE REMAINING ELEMENTS
ARE CALLED THE MINOR
MATRIX =>
-1 4
3 0

46. EXPANSION BY MINORS
EACH ELEMENT HAS A SIGN ASSOCIATED WITH IT FOR THE EXPANSION BY MINORS METHOD

47. EXPANSION BY MINORS 5 2 7 + - + -1 4 0 - + - 3 0 6
PICK ANY ROW OR COLUMN AND MULTIPLY EACH ELEMENT WITH IT’S RELATED SIGN BY THAT ELEMENT’S MINOR MATRIX AND ADD THE RESULTS

48. EXPANSION BY MINORS
PICK ANY ROW OR COLUMN AND MULTIPLY EACH ELEMENT WITH IT’S RELATED SIGN BY THAT ELEMENT’S MINOR MATRIX AND ADD THE RESULTS
4 0
0 6 =5

49. EXPANSION BY MINORS
PICK ANY ROW OR COLUMN AND MULTIPLY EACH LEMENT WITH IT’S RELATED SIGN BY THAT ELEMENT’S MINOR MATRIX AND ADD THE RESULTS
4 0
0 6 =5
-1 0
3 6
- 2

50. EXPANSION BY MINORS
PICK ANY ROW OR COLUMN AND MULTIPLY EACH ELEMENT WITH IT’S RELATED SIGN BY THAT ELEMENT’S MINOR MATRIX AND ADD THE RESULTS
-1 4
3 0
4 0
0 6
-1 0
3 6
= 5
- 2 +7

51. EXPANSION BY MINORS
PICK ANY ROW OR COLUMN AND MULTIPLY EACH ELEMENT WITH IT’S RELATED SIGN BY THAT ELEMENT’S MINOR MATRIX AND ADD THE RESULTS
-1 4
3 0
4 0
0 6
-1 0
3 6
= 5
- 2 +7
= 5(24-0)

52. EXPANSION BY MINORS
PICK ANY ROW OR COLUMN AND MULTIPLY EACH ELEMENT WITH IT’S RELATED SIGN BY THAT ELEMENT’S MINOR MATRIX AND ADD THE RESULTS
-1 4
3 0
4 0
0 6
-1 0
3 6
= 5
- 2 +7
= 5(24 - 0) – 2(-6 - 0)

53. EXPANSION BY MINORS
PICK ANY ROW OR COLUMN AND MULTIPLY EACH ELEMENT WITH IT’S RELATED SIGN BY THAT ELEMENT’S MINOR MATRIX AND ADD THE RESULTS
-1 4
3 0
4 0
0 6
-1 0
3 6
= 5
- 2 +7
= 5(24 - 0) – 2(-6 - 0) + 7(0 – 12)

54. EXPANSION BY MINORS
PICK ANY ROW OR COLUMN AND MULTIPLY EACH ELEMENT WITH IT’S RELATED SIGN BY THAT ELEMENT’S MINOR MATRIX AND ADD THE RESULTS
-1 4
3 0
4 0
0 6
-1 0
3 6
= 5
- 2 +7
= 5(24 - 0) – 2(-6 - 0) + 7(0 – 12)
= 5(24) – 2(-6) + 7(-12)

55. EXPANSION BY MINORS
PICK ANY ROW OR COLUMN AND MULTIPLY EACH ELEMENT WITH IT’S RELATED SIGN BY THAT ELEMENT’S MINOR MATRIX AND ADD THE RESULTS
-1 4
3 0
4 0
0 6
-1 0
3 6
= 5
- 2 +7
= 5(24 - 0) – 2(-6 - 0) + 7(0 – 12)
= 5(24) – 2(-6) + 7(-12) =

56. EXPANSION BY MINORS
PICK ANY ROW OR COLUMN AND MULTIPLY EACH ELEMENT WITH IT’S RELATED SIGN BY THAT ELEMENT’S MINOR MATRIX AND ADD THE RESULTS
-1 4
3 0
4 0
0 6
-1 0
3 6
= 5
- 2 +7
= 5(24 - 0) – 2(-6 - 0) + 7(0 – 12)
= 5(24) – 2(-6) + 7(-12) = = 48

57. EXPANSION BY MINORS
PICK ANY ROW OR COLUMN AND MULTIPLY EACH ELEMENT WITH IT’S RELATED SIGN BY THAT ELEMENT’S MINOR MATRIX AND ADD THE RESULTS EXAMPLE #2

58. EXPANSION BY MINORS
PICK ANY ROW OR COLUMN AND MULTIPLY EACH ELEMENT WITH IT’S RELATED SIGN BY THAT ELEMENT'S MINOR MATRIX AND ADDTHE RESULTS EXAMPLE #2
-1 0
3 6
- 2

59. EXPANSION BY MINORS
PICK ANY ROW OR COLUMN AND MULTIPLY EACH ELEMENT WITH IT’S RELATED SIGN BY THAT ELEMENT'S MINOR MATRIX AND ADD THE RESULTS
-1 0
3 6 +4 -2
5 7
3 6

60. EXPANSION BY MINORS
PICK ANY ROW OR COLUMN AND MULTIPLY EACH ELEMENT WITH IT’S RELATED SIGN BY THAT ELEMENT'S MINOR MATRIX AND ADD THE RESULTS
5 7
-1 0
-1 0
3 6
5 7
3 6
= -2
+ 4 -0

61. EXPANSION BY MINORS
PICK ANY ROW OR COLUMN AND MULTIPLY EACH ELEMENT WITH IT’S RELATED SIGN BY THAT ELEMENT'S MINOR MATRIX AND ADD THE RESULTS
5 7
-1 0
-1 0
3 6
5 7
3 6
= -2
+ 4 -0
= -2(-6 - 0) +4( ) - 0(0 – (-7))

62. EXPANSION BY MINORS
PICK ANY ROW OR COLUMN AND MULTIPLY EACH ELEMENT WITH IT’S RELATED SIGN BY THAT ELEMENT'S MINOR MATRIX AND ADD THE RESULTS
5 7
-1 0
-1 0
3 6
5 7
3 6
= -2
+ 4 -0
= -2(-6 - 0) +4( ) - 0(0 – (-7))
= -2(-6) + 4(9) - 0(-7)

63. EXPANSION BY MINORS
PICK ANY ROW OR COLUMN AND MULTIPLY EACH ELEMENT WITH IT’S RELATED SIGN BY THAT ELEMENT'S MINOR MATRIX AND ADD THE RESULTS
5 7
-1 0
-1 0
3 6
5 7
3 6
= -2
+ 4 -0
= -2(-6 - 0) +4( ) - 0(0 – (-7))
= -2(-6) + 4(9) - 0(-7) =

64. EXPANSION BY MINORS
PICK ANY ROW OR COLUMN AND MULTIPLY EACH ELEMENT WITH IT’S RELATED SIGN BY THAT ELEMENT'S MINOR MATRIX AND ADD THE RESULTS
5 7
-1 0
-1 0
3 6
5 7
3 6
= -2
+ 4 -0
= -2(-6 - 0) +4( ) - 0(0 – (-7))
= -2(-6) + 4(9) - 0(-7) = = 48

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to Beginning
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