Introduction to the MatrixGrab some paper and a pencil because we are going to do some learnin’ today!

Content

• What is a Matrix?

• What is it Used For?

• Describing a Matrix

• Matrix Addition

• Matrix Subtraction

What is… THE MATRIX?

▫ a rectangular array of objects

▫ way of organizing information

▫ matrix v. matrices

5419

3116

2118

972

▫ Elements

▫ Rows

▫ Columns

3 Key Features

5419

3116

2118

972

Describe the matrix

5419

3116

2118

972

• Dimensions = row x column

• Element notation = arc

• Example: a32 = ___

Check your work.

5419

3116

2118

972

• Dimensions = row x column

• Element notation = arc

• Example: a32 = 11

*This matrix has dimension 4x3.

What is a matrix used for?

5419

3116

2118

972

• To organize information

• How many jellybeans did Paulie get?

• Who got the most chocolate bars?

• What does the sum of the first row represent?

• What does the sum of the third column represent?

Mark

Janice

Paulie

Joyce

Chocolate Bars

Lollipops Jellybeans

Check your work.

5419

3116

2118

972

• To organize information

• How many jellybeans did Paulie get?3

• Who got the most chocolate bars?Joyce

• What does the sum of the first row represent?Mark’s total candy item count

• What does the sum of the third column represent?The number of jellybeans the group has all together

Mark

Janice

Paulie

Joyce

Chocolate Bars

Lollipops Jellybeans

What are the dimensions of…

6599

4511

766

53

8732

• Find elements a21 and a34 in both matrices.

54511526755

3521151787533

87984336733

50746788

Check your work.

6599

4511

766

53

8732

• Find elements a21 and a34 in both matrices.

The first matrix has a 3 in a21 and no element in a34.

The second matrix has a 33 in a21 and 17 in a34.

54511526755

3521151787533

87984336733

50746788

What if we have more than one?

5419

3116

2118

972

Mark

Janice

Paulie

Joyce

Chocolate Bars

Lollipops Jellybeans

281

8112

1724

1197

Matt

Jane

Pat

Joe

Chocolate Bars

Lollipops Jellybeans

Matrix Addition

• As long as the dimensions of the matrices are the same, finding their sum is as simple as adding the matching elements and creating a new matrix with that information!

5419

3116

2118

972

281

8112

1724

1197

2584119

83111126

17212148

1199772

71220

111218

38312

20119

Add!

• What do you notice about the sum of these matrices?

795

568

378

262

147

973

795

568

378

262

147

973

Check your work.

• What do you notice about the sum of these matrices?The sum is the same no matter the order of the matrices.

795

568

378

262

147

973

795

568

378

262

147

973

9157

61015

121411

9157

61015

121411

Matrix Subtraction

• As long as the dimensions of the matrices are the same, finding their difference is as simple as subtracting the matching elements and creating a new matrix with that information!

5419

3116

2118

972

281

8112

1724

1197

2584119

83111126

17212148

1199772

3418

5106

414

225

Subtract!

• What do you notice about the difference of these matrices?

795

568

378

262

147

973

795

568

378

262

147

973

Check your work.

• What do you notice about the difference of these matrices?The difference is the opposite when you switch the order of the matrices.

795

568

378

262

147

973

795

568

378

262

147

973

533

421

605

533

421

605

What if there’s more than two?

• Does the grouping matter?

19

13

17

811

53

72

19

13

17

811

53

72

Check your work.

• Does the grouping matter? No.

19

13

17

811

53

72

19

13

17

811

53

72

513

1616

513

1616

What if there’s more than two?

• Does the grouping matter?

19

13

17

811

53

72

19

13

17

811

53

72

Check your work.

• Does the grouping matter? Yes.

19

13

17

811

53

72

19

13

17

811

53

72

519

212

55

1410

Summary of Properties

• Matrix Addition is both commutative and associative.

• Matrix Subtraction is neither commutative nor associative.

• Its just like numerical addition and subtraction!

References

• Information in this presentation was created by Liz Wascher at Central Lake Public Schools.

• All images were retrieved from Microsoft PowerPoint clip art.