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Matrix Multiplication Sec. 4.2

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Presentation on theme: "Matrix Multiplication Sec. 4.2"— Presentation transcript:

1 Matrix Multiplication Sec. 4.2

2 Matrix Multiplication #1
3 5 -2 1 4 9 5 2 3 4 X = 3 x 2 2 x 2 Must be equal

3 Matrix Multiplication #1
3 5 -2 1 4 9 5 2 3 4 __ X = 3 x 2 2 x 2 3 x 2 The resulting matrix size

4 Matrix Multiplication #2
5 3 -2 4 -1 X 2 1 3 4 5 6 = 3 x 2 2 x 4 Must be equal

5 Matrix Multiplication #2
5 3 -2 4 -1 __ X 2 1 3 4 5 6 = 3 x 2 2 x 4 3 x 4 The resulting matrix size

6 Matrix Multiplication #3
2 5 -2 1 4 6 9 Can not multiply these matrices X 2 1 3 4 5 6 2 x 4 3 x 3 not equal

7 Matrix Multiplication
3 5 -2 1 4 9 5 2 3 4 X Row by Column

8 Let’s Begin……….

9 Row 1 X Column 1 3 5 -2 1 4 9 5 2 3 4 X 3 x x 3 = 30

10 Row 1 X Column 1 3 5 -2 1 4 9 5 2 3 4 X 3 x x 3 = 30

11 Row 1 X Column 1 3 5 -2 1 4 9 5 2 3 4 X 30 = A(1,1)

12 Row 1 X Column 2 3 5 -2 1 4 9 5 2 3 4 X 3 x x 4 = 26

13 Row 1 X Column 2 3 5 -2 1 4 9 5 2 3 4 X 3 x x 4 = 26

14 Row 1 X Column 2 3 5 -2 1 4 9 5 2 3 4 X 30 26 = A(1,2)

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

16 Row 2 X Column 1 3 5 -2 1 4 9 5 2 3 4 X -2 x x 3 = -7

17 Row 2 X Column 1 3 5 -2 1 4 9 5 2 3 4 X 30 26 -7 = A(2,1)

18 Row 2 X Column 2 3 5 -2 1 4 9 5 2 3 4 X -2 x x 4 = 0

19 Row 2 X Column 2 3 5 -2 1 4 9 5 2 3 4 X -2 x x 4 = 0

20 Row 2 X Column 2 3 5 -2 1 4 9 5 2 3 4 X 30 26 -7 = A(2,2)

21 Row 3 X Column 1 3 5 -2 1 4 9 5 2 3 4 X 4 x x 3 = 47

22 Row 3 X Column 1 3 5 -2 1 4 9 5 2 3 4 X 4 x x 3 = 47

23 Row 3 X Column 1 3 5 -2 1 4 9 5 2 3 4 X 30 26 -7 47 = A(3,1)

24 Row 3 X Column 2 3 5 -2 1 4 9 5 2 3 4 X 4 x x 4 = 44

25 Row 3 X Column 2 3 5 -2 1 4 9 5 2 3 4 X 4 x x 4 = 44

26 Row 3 X Column 2 3 5 -2 1 4 9 5 2 3 4 X 30 26 -7 47 44 = A(3,2)

27 A Quick Review

28 Row 1 X Column 1 3 5 -2 1 4 9 5 2 3 4 X 30 = A(1,1)

29 Row 1 X Column 2 3 5 -2 1 4 9 5 2 3 4 X 30 26 = A(1,2)

30 Row 2 X Column 1 3 5 -2 1 4 9 5 2 3 4 X 30 26 -7 = A(2,1)

31 Row 2 X Column 2 3 5 -2 1 4 9 5 2 3 4 X 30 26 -7 = A(2,2)

32 Row 3 X Column 1 3 5 -2 1 4 9 5 2 3 4 X 30 26 -7 47 = A(3,1)

33 Row 3 X Column 2 3 5 -2 1 4 9 5 2 3 4 X 30 26 -7 47 44 = A(3,2)

34 Matrix Multiplication
3 5 -2 1 4 9 5 2 3 4 X 30 26 -7 47 44 =

35 One Final Concept with Matrix Multiplication

36 Matrix Multiplication
Not Commutative

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