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4.3 Matrix Multiplication 1.Multiplying a Matrix by a Scalar 2.Multiplying Matrices.

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Presentation on theme: "4.3 Matrix Multiplication 1.Multiplying a Matrix by a Scalar 2.Multiplying Matrices."— Presentation transcript:

1 4.3 Matrix Multiplication 1.Multiplying a Matrix by a Scalar 2.Multiplying Matrices

2 1) Multiplying a Matrix by a Scalar The number or factor you multiply a matrix by is called a scalar. When multiplying by a scalar, every element in the matrix gets multiplied.

3 1) Multiplying a Matrix by a Scalar Example 1: Find 3 -2 -3 4 0 9 3.4 3 is a scalar

4 1) Multiplying a Matrix by a Scalar Example 1: Find 3 = -2 -3 4 0 9 3.4 -6 -9 12 0 27 10.2

5 1) Multiplying a Matrix by a Scalar Example 2: Find X. 6 9 -12 15 27 -18 30 6 = -3X + 2

6 1) Multiplying a Matrix by a Scalar Example 2: Find X. 6 9 -12 15 27 -18 30 6 = -3X + 2 12 18 -24 30 27 -18 30 6 = -3X +

7 1) Multiplying a Matrix by a Scalar Example 2: Find X. 6 9 -12 15 27 -18 30 6 = -3X + 2 12 18 -24 30 27 -18 30 6 = -3X + 12 18 -24 30 27 -18 30 6 = -3X -

8 1) Multiplying a Matrix by a Scalar Example 2: Find X. 6 9 -12 15 27 -18 30 6 = -3X + 2 12 18 -24 30 27 -18 30 6 = -3X + 15 -36 54 -24 = -3X

9 1) Multiplying a Matrix by a Scalar Example 2: Find X. 6 9 -12 15 27 -18 30 6 = -3X + 2 12 18 -24 30 27 -18 30 6 = -3X + -5 12 -18 8 = X

10 2) Multiplying Matrices Multiply the rows of the first matrix by the columns of the second matrix and add. Stay organized or it will get messy…fast.

11 2) Multiplying Matrices Example 1: Find the product of and -3 3 5 0 -1 0 3 -4

12 2) Multiplying Matrices Example 1: Find the product of and Answer:Some matrix with dimensions 2x2 -3 3 5 0 -1 0 3 -4 ? ? ?

13 2) Multiplying Matrices Example 1: Find the product of and -3 3 5 0 -1 0 3 -4 Multiply row 1 and column 1

14 2) Multiplying Matrices Example 1: Find the product of and =(-3)(-1) + 3(3) =12 -3 3 5 0 -1 0 3 -4 Multiply row 1 and column 1

15 2) Multiplying Matrices Example 1: Find the product of and =(-3)(-1) + 3(3) =12 -3 3 5 0 -1 0 3 -4 Multiply row 1 and column 1 12 ? ? ?

16 2) Multiplying Matrices Example 1: Find the product of and =(-3)(0) + 3(-4) =-12 -3 3 5 0 -1 0 3 -4 Multiply row 1 and column 2 12 ? ? ?

17 2) Multiplying Matrices Example 1: Find the product of and =(-3)(0) + 3(-4) =-12 -3 3 5 0 -1 0 3 -4 Multiply row 1 and column 2 12 -12 ? ?

18 2) Multiplying Matrices Example 1: Find the product of and =(5)(-1) + 0(3) =-5 -3 3 5 0 -1 0 3 -4 Multiply row 2 and column 1 12 -12 ? ?

19 2) Multiplying Matrices Example 1: Find the product of and =(5)(-1) + 0(3) =-5 -3 3 5 0 -1 0 3 -4 Multiply row 2 and column 1 12 -12 -5 ?

20 2) Multiplying Matrices Example 1: Find the product of and =(5)(0) + 0(-4) =0 -3 3 5 0 -1 0 3 -4 Multiply row 2 and column 2 12 -12 -5 ?

21 2) Multiplying Matrices Example 1: Find the product of and =(5)(0) + 0(-4) =0 -3 3 5 0 -1 0 3 -4 Multiply row 2 and column 2 12 -12 -5 0

22 2) Multiplying Matrices Example 2: Find the product of and -3 3 5 0 -1 0 3 -4

23 2) Multiplying Matrices Example 2: Find the product of and -3 3 5 0 -1 0 3 -4 ? ?

24 2) Multiplying Matrices Example 2: Find the product of and -3 3 5 0 -1 0 3 -4 ? ?

25 2) Multiplying Matrices Example 2: Find the product of and =(-1)(-3) + (0)(5) =3 -3 3 5 0 -1 0 3 -4 ? ?

26 2) Multiplying Matrices Example 2: Find the product of and =(-1)(-3) + (0)(5) =3 -3 3 5 0 -1 0 3 -4 3 ? ? ?

27 2) Multiplying Matrices Example 2: Find the product of and =(-1)(3) + (0)(5) =-3 -3 3 5 0 -1 0 3 -4 3 ? ? ?

28 2) Multiplying Matrices Example 2: Find the product of and =(-1)(3) + (0)(5) =-3 -3 3 5 0 -1 0 3 -4 3 -3 ? ?

29 2) Multiplying Matrices Example 2: Find the product of and =(3)(-3) + (-4)(5) =-29 -3 3 5 0 -1 0 3 -4 3 -3 ? ?

30 2) Multiplying Matrices Example 2: Find the product of and =(3)(-3) + (-4)(5) =-29 -3 3 5 0 -1 0 3 -4 3 -3 -29 ?

31 2) Multiplying Matrices Example 2: Find the product of and =(3)(3) + (-4)(0) =9 -3 3 5 0 -1 0 3 -4 3 -3 -29 ?

32 2) Multiplying Matrices Example 2: Find the product of and =(3)(3) + (-4)(0) =9 -3 3 5 0 -1 0 3 -4 3 -3 -29 9

33 4.2 Quiz Prep p.180 #35-38

34 4.2 Quiz Prep Answers p.180 #35-38 35) B 36) G 37) x = 4, y = -2, w = 0, z = 6 38)x = 5, y = 1

35 2) Multiplying Matrices Example 3: Find the product of A = and B = -2 5 2 5 0.5 1 -3 7 4 2

36 2) Multiplying Matrices Example 3: Find the product of A = and B = **The matrices are different dimensions -2 5 2 5 0.5 1 -3 7 4 2

37 2) Multiplying Matrices Example 3: Find the product of A = and B = **The matrices are different dimensions **How do you know if a matrix product exists? -2 5 2 5 0.5 1 -3 7 4 2

38 2) Multiplying Matrices Example 3: Find the product of A = and B = -2 5 2 5 0.5 1 -3 7 4 2 ABBA (2 x 2)(2 x 3)(2 x 3)(2 x 2)

39 2) Multiplying Matrices Example 3: Find the product of A = and B = -2 5 2 5 0.5 1 -3 7 4 2 ABBA (2 x 2)(2 x 3)(2 x 3)(2 x 2)

40 2) Multiplying Matrices Example 3: Find the product of A = and B = -2 5 2 5 0.5 1 -3 7 4 2 ABBA (2 x 2)(2 x 3)(2 x 3)(2 x 2)

41 2) Multiplying Matrices Example 3: Find the product of A = and B = -2 5 2 5 0.5 1 -3 7 4 2 ABBA (2 x 2)(2 x 3)(2 x 3)(2 x 2) Columns of A match rows of B Columns of B do not match rows of A

42 2) Multiplying Matrices Example 3: Find the product of A = and B = -2 5 2 5 0.5 1 -3 7 4 2 ABBA (2 x 2)(2 x 3)(2 x 3)(2 x 2) Columns of A match rows of B Columns of B do not match rows of A Product AB is defined Product BA is undefined

43 2) Multiplying Matrices Example 3: Find the product of A = and B = Dimensions of the product matrix =(2 x 2)(2 x 3) -2 5 2 5 0.5 1 -3 7 4 2

44 2) Multiplying Matrices Example 3: Find the product of A = and B = Dimensions of the product matrix =(2 x 2)(2 x 3) -2 5 2 5 0.5 1 -3 7 4 2

45 2) Multiplying Matrices Example 3: Find the product of A = and B = Dimensions of the product matrix =(2 x 2)(2 x 3) =(2 x 3) -2 5 2 5 0.5 1 -3 7 4 2

46 2) Multiplying Matrices Example 3: Find the product of A = and B = -3(-2) + 7(5)-3(5) + 7(0.5)-3(2) + 7(1) = 4(-2) + 2(5)4(5) + 2(0.5)4(2) + 2(1) -2 5 2 5 0.5 1 -3 7 4 2

47 2) Multiplying Matrices Example 3: Find the product of A = and B = 41-11.51 = 2 21 10 -2 5 2 5 0.5 1 -3 7 4 2

48 2) Multiplying Matrices Example 4: Find the product of B = and A = -2 5 2 5 0.5 1 -3 7 4 2

49 2) Multiplying Matrices Example 4: Find the product of B = and A = =(2 x 3)(2 x 2) = undefined -2 5 2 5 0.5 1 -3 7 4 2

50 Homework p.186 #5, 7, 10, 13-15, 19, 20-24, 40, 51 Tomorrow In-class assignment Friday Quiz – section 4.3

51 Select Homework Solutions p.186 #5, 7, 10, 13-15, 19, 20-24, 40, 51 14) [34]23) Undefined 15) [34 0]24) Defined 20) Defined51) x = -3, y = -9 21) Defined 22) Defined

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