Do matrix multiplication by definition count how many additi

Do matrix multiplication \"by definition count how many additions and multiplication operations you do on the way: (2 5 17 7) (4 3 9 12) of additions: of multiplications: (2 5 2 6 17 7 5 4 3 2 4 3 1 1 19 1) (4 3 8 3 9 12 1 1 1 2 2 1 4 1 5 3) of additions: of multiplications:

Solution

So. lets start by multiplying the Matrices

a)

Matrix A

Matrix B

c11 = 2 x 4 + 5 x 9 = 53

c12 = 2 x 3 + 5 x 12 = 66

c21 = 17 x 4 + 7 x 9 = 131

c22 = 17 x 3 + 7 x 12 = 135

So each Step has 2 Multiplications and we have 4 steps so 2*4=8 Multiplications.

and each step has 1 addition and we have 4 steps so 1*4=4 Additions.

# of Additions=4

# of Multiplications=8

b)

Matrix A

A1

A2

A3

A4

1

2

5

2

6

2

17

7

5

4

3

3

2

4

3

4

1

1

19

1

Matrix B

B1

B2

B3

B4

1

4

3

8

3

2

9

12

1

1

3

1

2

2

1

4

4

1

5

3

c11 = 2 x 4 + 5 x 9 + 2 x 1 + 6 x 4 = 79

C1

C2

C3

C4

1

79

0

0

0

2

0

0

0

0

3

0

0

0

0

4

0

0

0

0

c12 = 2 x 3 + 5 x 12 + 2 x 2 + 6 x 1 = 76

C1

C2

C3

C4

1

79

76

0

0

2

0

0

0

0

3

0

0

0

0

4

0

0

0

0

c13 = 2 x 8 + 5 x 1 + 2 x 2 + 6 x 5 = 55

C1

C2

C3

C4

1

79

76

55

0

2

0

0

0

0

3

0

0

0

0

4

0

0

0

0

c14 = 2 x 3 + 5 x 1 + 2 x 1 + 6 x 3 = 31

C1

C2

C3

C4

1

79

76

55

31

2

0

0

0

0

3

0

0

0

0

4

0

0

0

0

c21 = 17 x 4 + 7 x 9 + 5 x 1 + 4 x 4 = 152

C1

C2

C3

C4

1

79

76

55

31

2

152

0

0

0

3

0

0

0

0

4

0

0

0

0

c22 = 17 x 3 + 7 x 12 + 5 x 2 + 4 x 1 = 149

C1

C2

C3

C4

1

79

76

55

31

2

152

149

0

0

3

0

0

0

0

4

0

0

0

0

c23 = 17 x 8 + 7 x 1 + 5 x 2 + 4 x 5 = 173

C1

C2

C3

C4

1

79

76

55

31

2

152

149

173

0

3

0

0

0

0

4

0

0

0

0

c24 = 17 x 3 + 7 x 1 + 5 x 1 + 4 x 3 = 75

C1

C2

C3

C4

1

79

76

55

31

2

152

149

173

75

3

0

0

0

0

4

0

0

0

0

c31 = 3 x 4 + 2 x 9 + 4 x 1 + 3 x 4 = 46

C1

C2

C3

C4

1

79

76

55

31

2

152

149

173

75

3

46

0

0

0

4

0

0

0

0

c32 = 3 x 3 + 2 x 12 + 4 x 2 + 3 x 1 = 44

C1

C2

C3

C4

1

79

76

55

31

2

152

149

173

75

3

46

44

0

0

4

0

0

0

0

c33 = 3 x 8 + 2 x 1 + 4 x 2 + 3 x 5 = 49

C1

C2

C3

C4

1

79

76

55

31

2

152

149

173

75

3

46

44

49

0

4

0

0

0

0

c34 = 3 x 3 + 2 x 1 + 4 x 1 + 3 x 3 = 24

C1

C2

C3

C4

1

79

76

55

31

2

152

149

173

75

3

46

44

49

24

4

0

0

0

0

c41 = 1 x 4 + 1 x 9 + 19 x 1 + 1 x 4 = 36

C1

C2

C3

C4

1

79

76

55

31

2

152

149

173

75

3

46

44

49

24

4

36

0

0

0

c42 = 1 x 3 + 1 x 12 + 19 x 2 + 1 x 1 = 54

C1

C2

C3

C4

1

79

76

55

31

2

152

149

173

75

3

46

44

49

24

4

36

54

0

0

c43 = 1 x 8 + 1 x 1 + 19 x 2 + 1 x 5 = 52

C1

C2

C3

C4

1

79

76

55

31

2

152

149

173

75

3

46

44

49

24

4

36

54

52

0

c44 = 1 x 3 + 1 x 1 + 19 x 1 + 1 x 3 = 26

C1

C2

C3

C4

1

79

76

55

31

2

152

149

173

75

3

46

44

49

24

4

36

54

52

26

So. on each step we have 4 multiplications, and we have 16 steps, so we will have 16*4=64 Multiplications

and on each step we have 3 additions so for 16 steps we have 16*3=48 Additions.

# of Additions= 48

# of Multiplications= 64.

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	A1	A2
1	2	5
2	17	7