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

4.3 Matrix Multiplication

1. Multiplying a Matrix by a Scalar

2. Multiplying Matrices

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.

Example 1:

Find 3-2 -3 4

0 9 3.4

3 is a scalar

Example 1:

Find 3

-2 -3 4

0 9 3.4

-6 -9 12

0 27 10.2

Example 2: Find X.

-12 15

27 -18

30 6=-3X + 2

Example 2: Find X.

-12 15

27 -18

30 6=-3X + 2

-24 30

27 -18

30 6=-3X +

Example 2: Find X.

-12 15

27 -18

30 6=-3X + 2

-24 30

27 -18

30 6=-3X +

-24 30

27 -18

=-3X -

Example 2: Find X.

-12 15

27 -18

30 6=-3X + 2

-24 30

27 -18

30 6=-3X +

15 -36

54 -24

Example 2: Find X.

-12 15

27 -18

30 6=-3X + 2

-24 30

27 -18

30 6=-3X +

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.

Example 1:

Find the product of and-3 3

Example 1:

Find the product of and

Answer: Some matrix with dimensions 2x2

Example 1:

Multiply row 1 and column 1

Example 1:

= (-3)(-1) + 3(3)

Example 1:

= (-3)(-1) + 3(3)

Example 1:

= (-3)(0) + 3(-4)

Example 1:

= (-3)(0) + 3(-4)

12 -12

Example 1:

= (5)(-1) + 0(3)

12 -12

Example 1:

= (5)(-1) + 0(3)

12 -12

Example 1:

= (5)(0) + 0(-4)

12 -12

Example 1:

= (5)(0) + 0(-4)

12 -12

Example 2:

= (-1)(-3) + (0)(5)

Example 2:

= (-1)(-3) + (0)(5)

Example 2:

= (-1)(3) + (0)(5)

Example 2:

= (-1)(3) + (0)(5)

Example 2:

= (3)(-3) + (-4)(5)

Example 2:

= (3)(-3) + (-4)(5)

Example 2:

= (3)(3) + (-4)(0)

Example 2:

= (3)(3) + (-4)(0)

4.2 Quiz Prep

p.180 #35-38

4.2 Quiz Prep Answers

p.180 #35-38

37) x = 4, y = -2, w = 0, z = 6

38) x = 5, y = 1

Example 3:

Find the product of A = and B =-2 5 2

5 0.5 1

Example 3:

Find the product of A = and B =

**The matrices are different dimensions

-2 5 2

5 0.5 1

Example 3:

**The matrices are different dimensions

**How do you know if a matrix product exists?

-2 5 2

5 0.5 1

Example 3:

Find the product of A = and B = -2 5 2

5 0.5 1

(2 x 2)(2 x 3) (2 x 3)(2 x 2)

Example 3:

5 0.5 1

(2 x 2)(2 x 3) (2 x 3)(2 x 2)

Example 3:

5 0.5 1

(2 x 2)(2 x 3) (2 x 3)(2 x 2)

Example 3:

5 0.5 1

(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

Example 3:

5 0.5 1

(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

Example 3:

Dimensions of the product matrix

= (2 x 2)(2 x 3)

-2 5 2

5 0.5 1

Example 3:

= (2 x 2)(2 x 3)

-2 5 2

5 0.5 1

Example 3:

= (2 x 2)(2 x 3)

= (2 x 3)

-2 5 2

5 0.5 1

Example 3:

-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

Example 3:

41 -11.5 1

2 21 10

-2 5 2

5 0.5 1

Example 4:

Find the product of B = and A =-2 5 2

5 0.5 1

Example 4:

Find the product of B = and A =

= (2 x 3)(2 x 2)

= undefined

-2 5 2

5 0.5 1

Homework

p.186 #5, 7, 10, 13-15, 19, 20-24, 40, 51

Tomorrow

In-class assignment

Friday

Quiz – section 4.3

Select Homework Solutions

p.186 #5, 7, 10, 13-15, 19, 20-24, 40, 51

14) [34] 23) Undefined15) [34 0] 24) Defined20) Defined 51) x = -3, y = -921) Defined22) Defined

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

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