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MATRICES - PowerPoint PPT Presentation


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MATRICES A rectangular array of numbers enclosed in a square brackets (or parentheses) is called a matrix (the plural is matrices) The entries of a matrix are called elements . Example #1 Consider the following two matrices. Is there any difference between them?

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matrices

MATRICES

A rectangular array of numbers enclosed in a square brackets (or parentheses) is called a matrix (the plural is matrices)

The entries of a matrix are called elements.

slide2

Example #1

Consider the following two matrices. Is there any difference between them?

Yes! M has 3 rows and 2 columns whereas N has 2 rows and 3 columns

slide3

Order of a matrix

If a matrix has m rows and n columns, we say that it is a matrix of order m X n, read m by n.

We also refer to it as an m X n matrix.

The first number (m) refers to the number of rows and the second number (n) to the number of columns.

slide4

Example #2

Find the order of each of the following matrices:

2 X 3

1 X 4

3 X 1

slide5

Matrix Operations

Now that we know the basic notions about matrices, we next consider how to perform operations with them.

Addition

We add matrices by adding corresponding elements.

slide6

Subtraction

We subtract matrices by subtracting corresponding elements.

Remark: To add or subtract matrices, they must have the same order.

Multiplication by a number

To multiply a matrix by a number, we multiply each element of the matrix by the number.

slide7

Example #3

Compute:

where

The matrices have the same order, so they can be added.

slide9

where

Since the matrices have the same order, they can be added.

slide10

where

Since the matrices don’t have the same order, we cannot compute their difference.

slide11

Equalityof matrices

  • Two matrices are equal if
  • they have the same order and
  • their corresponding elements are the same
slide12

Example #4

Find x and y if :

slide13

Example #5

The monthly expenditures (in dollars) for entertainment (E), food (F), and housing (H) per person under 25 and 25-34 years old are as show

What would be the annual expenditures in the categories under 25 and 25-34?

slide14

To find the annual expenditures, we multiply the given matrix by 12 (since there are 12 months in a year) and obtain