Adding and Subtracting Matrices

Section 2.4

Definition: Matrix

A matrix is a rectangular arrangement of numbers into horizontal rows and vertical columns.

Each number is called an entry or an element.

Matrices, though they may appear weird objects at first, are a very important tool in expressing and discussing problems which arise from real life cases.

A matrix is a grid, with each location in the grid containing some information. For example, a chess board is a matrix in which every square contains a specific item of information: a particular chess piece, or the lack of a chess piece.

Matrices

What is the size of a matrix?(the number of rows) x (the number of columns)

The matrix above is a 3 x 4 matrix because it has three rows and four columns.

6

2

8

3

4

0

7

2

1

5

1

3

Two Matrices are equal if the entries in corresponding

positions are equal.

Are these matrices equal?Why?

Of course this means that if two matrices are equal, then they must have the same numbers of rows and columns as each other. So a 3x3 matrix could never be equal to a 2x4 matrix, for instance.

Also remember that each element must be equal to that element in the other matrix, so it's no good if all the values are there but in different places.

Equal?

Writing Matrices

Write a matrix to organize the following information about your CD collection.

Country: 4 groups, 6 solo artists, 0 collections

Rock: 8 groups, 3 solo artists, 3 collections

Blues: 1 group, 5 solo artists, 2 collections

Writing MatricesCountry, Rock, and Blues can be labels for the rows or for the columns.

As Row Labels:

Group Solo CollectionCountryRockBlues

Writing MatricesCountry, Rock, and Blues can be labels for the rows or for the columns.

As Column Labels:

Country Rock BluesGroupSoloCollection

Write a matrix to organize the following information about the menus

at each school in a town.

High school: 5 entrees, 3 desserts, 5 drinks

Middle school: 3 entrees, 2 desserts, 4 drinks

Elementary school: 2 entrees, 2 desserts, 2 drinks

High school, Middle school, and Elementary school can be labels for the

rows or for the columns.

As Row Labels:

Entrees Desserts DrinksHigh school

Middle school

Elementary school

As Column Labels:

High Middle ElementaryEntrees

Desserts

Drinks

Adding and Subtracting Matrices

To add or subtract matrices, you add or subtract corresponding entries. Each matrix must have the same number of rows and columns.

Question: Can you add a matrix that has three rows to a matrix that has only two rows?

Adding and Subtracting Matrices

3

4

2

1

2

5

4

1

0

6

2

1

1

3

2

5

0

4

Adding and Subtracting Matrices

2__

____

23

54

05

610

Example #1

Example #1

Example #2

Example #2