1. Matrix Multiplication
Example 1
By: Jeffrey Bivin
Lake Zurich High School

2. Matrix Multiplication3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X
Row by Column

3. Matrix Multiplication3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X
Rows of the first matrix by
Columns of the second matrix

4. Matrix Multiplication3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X
Rows of the first matrix by
Columns of the second matrix

5. Matrix Multiplication3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X
Rows of the first matrix by
Columns of the second matrix
Jeff Bivin -- LZHS

6. Matrix Multiplication3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X
Rows of the first matrix by
Columns of the second matrix

7. Matrix Multiplication3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X
Rows of the first matrix by
Columns of the second matrix

8. Matrix Multiplication3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X
Rows of the first matrix by
Columns of the second matrix

9. Matrix Multiplication3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X
Rows of the first matrix by
Columns of the second matrix

10. Matrix Multiplication3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X
Rows of the first matrix by
Columns of the second matrix

11. Matrix Multiplication3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X
Rows of the first matrix by
Columns of the second matrix

12. Let’s Begin……….

13. Row 1 x Column 1 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X
3 x x x 2 = 25

14. Row 1 x Column 1 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X
3 x x x 2 = 25

15. Row 1 x Column 1 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X
3 x x x 2 = 25

16. Row 1 x Column 1 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 25 =
A(1,1)

17. 3 x (-1) + 2 x 3 + 5 x 7 = 38 X Row 1 x Column 2 3 2 5 -2 1 4 6 9 5 -11 4 6 9 5 -1 2 3 7 4 X
3 x (-1) + 2 x x 7 = 38

18. 3 x (-1) + 2 x 3 + 5 x 7 = 38 X Row 1 x Column 2 3 2 5 -2 1 4 6 9 5 -11 4 6 9 5 -1 2 3 7 4 X
3 x (-1) + 2 x x 7 = 38

19. 3 x (-1) + 2 x 3 + 5 x 7 = 38 X Row 1 x Column 2 3 2 5 -2 1 4 6 9 5 -11 4 6 9 5 -1 2 3 7 4 X
3 x (-1) + 2 x x 7 = 38

20. Row 1 x Column 2 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 25 38 =
A(1,2)

21. Row 1 x Column 3 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X
3 x x x 4 = 40

22. Row 1 x Column 3 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X
3 x x x 4 = 40

23. Row 1 x Column 3 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X
3 x x x 4 = 40

24. Row 1 x Column 3 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 25 38 40 =
A(1,3)

25. -2 x 5 + 0 x 0 + 1 x 2 = -8 X Row 2 x Column 1 3 2 5 -2 1 4 6 9 5 -1 21 4 6 9 5 -1 2 3 7 4 X
-2 x x x 2 = -8

26. -2 x 5 + 0 x 0 + 1 x 2 = -8 X Row 2 x Column 1 3 2 5 -2 1 4 6 9 5 -1 21 4 6 9 5 -1 2 3 7 4 X
-2 x x x 2 = -8

27. -2 x 5 + 0 x 0 + 1 x 2 = -8 X Row 2 x Column 1 3 2 5 -2 1 4 6 9 5 -1 21 4 6 9 5 -1 2 3 7 4 X
-2 x x x 2 = -8

28. Row 2 x Column 1 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 25 38 40 -8 =
A(2,1)

29. Row 2 x Column 2 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X

30. -2 x (-1) + 0 x 3 + 1 x 7 = 9 X Row 2 x Column 2 3 2 5 -2 1 4 6 9 5 -11 4 6 9 5 -1 2 3 7 4 X
-2 x (-1) + 0 x x 7 = 9

31. -2 x (-1) + 0 x 3 + 1 x 7 = 9 X Row 2 x Column 2 3 2 5 -2 1 4 6 9 5 -11 4 6 9 5 -1 2 3 7 4 X
-2 x (-1) + 0 x x 7 = 9

32. -2 x (-1) + 0 x 3 + 1 x 7 = 9 X Row 2 x Column 2 3 2 5 -2 1 4 6 9 5 -11 4 6 9 5 -1 2 3 7 4 X
-2 x (-1) + 0 x x 7 = 9
Jeff Bivin -- LZHS

33. Row 2 x Column 2 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 25 38 40 -8 9 =
A(2,2)

34. -2 x 2 + 0 x 7 + 1 x 4 = 0 X Row 2 x Column 3 3 2 5 -2 1 4 6 9 5 -1 21 4 6 9 5 -1 2 3 7 4 X
-2 x x x 4 = 0
Jeff Bivin -- LZHS

35. -2 x 2 + 0 x 7 + 1 x 4 = 0 X Row 2 x Column 3 3 2 5 -2 1 4 6 9 5 -1 21 4 6 9 5 -1 2 3 7 4 X
-2 x x x 4 = 0
Jeff Bivin -- LZHS

36. -2 x 2 + 0 x 7 + 1 x 4 = 0 X Row 2 x Column 3 3 2 5 -2 1 4 6 9 5 -1 21 4 6 9 5 -1 2 3 7 4 X
-2 x x x 4 = 0

37. Row 2 x Column 3 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 25 38 40 -8 9 =
A(2,3)
Jeff Bivin -- LZHS

38. Row 3 x Column 1 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X
4 x x x 2 = 38
Jeff Bivin -- LZHS

39. Row 3 x Column 1 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X
4 x x x 2 = 38

40. Row 3 x Column 1 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X
4 x x x 2 = 38

41. Row 3 x Column 1 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 25 38 40 -8 9 =
A(3,1)

42. 4 x (-1) + 6 x 3 + 9 x 7 = 77 X Row 3 x Column 2 3 2 5 -2 1 4 6 9 5 -11 4 6 9 5 -1 2 3 7 4 X
4 x (-1) + 6 x x 7 = 77
Jeff Bivin -- LZHS

43. 4 x (-1) + 6 x 3 + 9 x 7 = 77 X Row 3 x Column 2 3 2 5 -2 1 4 6 9 5 -11 4 6 9 5 -1 2 3 7 4 X
4 x (-1) + 6 x x 7 = 77

44. 4 x (-1) + 6 x 3 + 9 x 7 = 77 X Row 3 x Column 2 3 2 5 -2 1 4 6 9 5 -11 4 6 9 5 -1 2 3 7 4 X
4 x (-1) + 6 x x 7 = 77

45. Row 3 x Column 2 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 25 38 40 -8 9 77 =
A(3,2)

46. Row 3 x Column 3 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X
4 x x x 4 = 86

47. Row 3 x Column 3 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X
4 x x x 4 = 86

48. Row 3 x Column 3 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X
4 x x x 4 = 86
Jeff Bivin -- LZHS

49. Row 3 x Column 3 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 25 38 40 -8 9 77 86
A(3,3)

50. Matrix Multiplication3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 25 38 40 -8 9 77 86 =

51. Matrix Multiplication3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 25 38 40 -8 9 77 86 =

52. Matrix Multiplication3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 25 38 40 -8 9 77 86 =

53. A Quick Review

54. Row 1 x Column 1 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 25 =
A(1,1)

55. Row 1 x Column 2 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 25 38 =
A(1,2)

56. Row 1 x Column 3 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 25 38 40 =
A(1,3)

57. Row 2 x Column 1 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 25 38 40 -8 =
A(2,1)

58. Row 2 x Column 2 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 25 38 40 -8 9 =
A(2,2)

59. Row 2 x Column 3 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 25 38 40 -8 9 =
A(2,3)

60. Row 3 x Column 1 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 25 38 40 -8 9 =
A(3,1)

61. Row 3 x Column 2 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 25 38 40 -8 9 77 =
A(3,2)

62. Row 3 x Column 3 3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 25 38 40 -8 9 77 86 =
A(3,3)

63. Matrix Multiplication3 2 5 -2 1 4 6 9 5 -1 2 3 7 4 X 25 38 40 -8 9 77 86 =