Today:• Return C3 Test• Goal Evaluation• 4.1 Matrices• Calculator Activity• Finish 4.1

Instruction• Practice

Optimism is the faith that leads to achievement. Nothing can be done without hope and confidence.

Helen Keller

Integrated

Objectives:1. Identify the characteristics of a matrix.2. Add and subtract matrices.3. Solve matrix equations.4. Use matrices in a real life example. Vocabulary: row, column, row matrix, column matrix,

square matrix, zero matrix, scalar, matrix equation

Matrix Operations4.1

Matrix Operations4.1

A is a 2x3 matrix.

210

246A

1 3 5 7B =

2 4 6 8

Anatomy of a Matrix (Matrices)

Identify this matrix:

2 x 3

Matrix Operations4.1

A is a 2x3 matrix.

210

246A

Identify this matrix:

Anatomy of a Matrix (Matrices)

119422

30411

11023

C

3 x 5

Matrix Operations4.1

A is a 2x3 matrix.

210

246A

Identify this matrix:

Anatomy of a Matrix (Matrices)

210

412

312

132

D

4 x 3

Matrix Operations4.1

A is a 2x3 matrix.

210

246A

Identify this matrix:

Anatomy of a Matrix (Matrices)

7

2

3

Ecolumn matrix

3 x 1

Matrix Operations4.1

A is a 2x3 matrix.

210

246A

Identify this matrix:

Anatomy of a Matrix (Matrices)

row matrix

0232F

1 x 4

Matrix Operations4.1

A is a 2x3 matrix.

210

246A

Identify this matrix:

Anatomy of a Matrix (Matrices)

square matrix

321

310

543

G

3 x 3

Matrix Operations4.1

A is a 2x3 matrix.

210

246A

Identify this matrix:

Anatomy of a Matrix (Matrices)

zero matrix

00

00

00

H

3 x 2

Write a matrix to organize the following information about school lunch menus.

High School: 5 entrees, 3 desserts, 5 drinks

Middle School: 3 entrees, 2 desserts, 4 drinks

Example 1 Writing a Matrix

423

435

45

23

35

Matrix Operations4.1

210

246A

Each entry has its own address. (row, column)

Matrix Operations4.1

210

246A

Each entry has its own address. (row, column)

1,1

2,1 2,2

1,2 1,3

2,3

119422

30411

11023

C

210

246A

Matrices are equal if they are the same size and each entry is equal.

210

246B

c1b

24aJ

If A = J, then find the value of the variables.

Example 2 Find for Variables in a Matrix

210

246A

Matrices are equal if they are the same size and each entry is equal.

210

246B

If A = K, then find the value of the variables.

3-y1x

242zK

Example 2 Find for Variables in a Matrix

Matrix Operations4.1

Calculator Activity

210

246L

To add or subtract matrices:1. matrices same size2. add/subtract same entries

3-810

226-M

12

43N

51

00

23

P

10

52Q

523

024R

Find:L + M

Example 3 Adding and Subtracting Matrices

1910

460ML

210

246L

To add or subtract matrices:1. matrices same size2. add/subtract same entries

3-810

226-M

12

43N

51

00

23

P

10

52Q

523

024R

Find:M + N

Example 3 Adding and Subtracting Matrices

Can’t be done.

210

246L

To add or subtract matrices:1. matrices same size2. add/subtract same entries

3-810

226-M

12

43N

51

00

23

P

10

52Q

523

024R

Find:N + R

Example 3 Adding and Subtracting Matrices

Can’t be done.

210

246L

To add or subtract matrices:1. matrices same size2. add/subtract same entries

3-810

226-M

12

43N

51

00

23

P

10

52Q

523

024R

Find: M – R

Example 3 Adding and Subtracting Matrices

81013

202RM

210

246L

To add or subtract matrices:1. matrices same size2. add/subtract same entries

3-810

226-M

12

43N

51

00

23

P

10

52Q

523

024R

Find: P – L

Example 3 Adding and Subtracting Matrices

Can’t be done.

210

246L

To add or subtract matrices:1. matrices same size2. add/subtract same entries

3-810

226-M

12

43N

51

00

23

P

10

52Q

523

024R

Find: Q – N

Example 3 Adding and Subtracting Matrices

02

11NQ

Congress: The United States Congress is Congress: The United States Congress is composed of the House of composed of the House of Representatives and the Senate. The Representatives and the Senate. The matrices below show the number of men matrices below show the number of men and women in the Senate and House in and women in the Senate and House in 1999 for 1061999 for 106thth Congress. Write and label Congress. Write and label a single matrix that show the number of a single matrix that show the number of men and women in Congressmen and women in Congress

Example 4 Real World: US Congress

01

17206

39172

Other

Repulican

Democrat

WomenMen

00

352

639

Other

Repulican

Democrat

WomenMenHouse Senate

01

20258

45211

Other

Repulican

Democrat

WomenMen

Profit: You own two stores that sell household appliances. The matrices below show revenue and expenses for three months at each store

Example 4 Real World: Profit Matrix

118,78294,311

120,42982,529

109,34578,432

March

February

January

2Store1StoreRevenue $

120,83385,456

104,97264,372

98,45954,426

March

February

January

2Store1StoreExpenses $

2,0518,855

15,45718,157

10,88619,006

March

February

January

2Store1StoreProfit $

To multiply a scalar:1. Multiply the scalar with every

entry

Perform the scalar multiplication:

210

2466

21

343-

Example 5 Multiply a Matrix by a Scalar

To solve a matrix equation:1. Simplify both sides of the

equation.2. Set up equations and solve3. Present answers4. Check

Solve:

80

48-48

61

2x-4

2y1-

084

x = 6, y = -2

Example 6 Solve a Matrix Equation

To solve a matrix equation:1. Simplify both sides of the

equation.2. Set up equations and solve3. Present answers4. Check

Solve:

2118

9-0

11-

5x

4y5

2103

x = 10, y = 2

Example 6 Solve a Matrix Equation

Assignment:• 4.1 p89 #7-25, 27,

28 • Progress Report

Signature

Optimism is the faith that leads to achievement. Nothing can be done without hope and confidence.

Helen Keller

Integrated