objectives add two matrices subtract two matrices multiply a matrix by a constant multiply two...

Mat 150 – Class #23

Objectives

Add two matricesSubtract two matricesMultiply a matrix by a constantMultiply two matrices

Matrix AdditionThe sum of two matrices with the same dimensions is the matrix that is formed by adding the corresponding entries of the two matrices. Addition is not definedif the matrices do not have the same number of rows and the same number of columns.

Example

Find the following sums of matrices.a.

b.

a b w y

c d x z

1 3 8 0 1 4 2 4

3 6 1 3 5 2 4 2

4 5 3 2 5 1 4 1

Example (cont)

Find the following sums of matrices.c. A + B if

A + B =

The matrix that is the sum is called the ________matrix.

2 3 2 3 and

1 4 1 4A B

2 3 2 3

1 4 1 4

Matrix SubtractionIf matrices M and N have the same dimension, the difference M N is found by subtracting the elements of N from the corresponding elements of M. This differencecan also be defined as

M N = M + ( N)

Example

Complete the following matrix operations.a.

b.

2 1 3 1 2 4

5 4 2 5 2 3

1 4 2 6 2 3

1 4 5 2 2 3

3 6 3 5 4 8

2 1 12 3 2 0

Product of a Number and a MatrixMultiplying a matrix A by a real number c results in a matrix in which each entry of matrix A is multiplied by the number c.

Example

The table contains the purchase prices and delivery costs (per unit) for plywood, siding, and lumber. If the supplier announces a 5% increase in all of these prices and in delivery costs, find the matrix that gives the new prices and costs.

Example (cont)

Use a matrix to represent the original prices and costs.

32 23 2.60

3 1 0.60

Example

Compute the products AB and BA for the matrices1 2

and .3 4

a bA B

c d

Example

A business plans to use three methods of advertising—newspapers, radio, and cable TV—in each of its two markets, I and II. The cost per ad type in each market (in thousands of dollars) is given by matrix A. The business has three target groups: teenagers, single women, and men aged 35 to 50. Matrix B gives the number of ads per week directed at each of these groups.a. Does AB or BA give the matrix that represents the cost of ads

for each target group in each market?b. Find this matrix.c. For what group of people is the most money spent on

advertising?

Example (cont)

a. Does AB or BA give the matrix that represents the cost of ads for each target group in each market?

b. Find this matrix.

Example (cont)

3 12 15 12 10

5 16 10 10 8

10 11 6 5 9

BA

Example (cont)

c. For what group of people is the most money spent on advertising?

Example

Use technology to compute BA and AB if

2 4 11 2

3 2 10 1 and

2 0 23 2

1 3 0

A B

Example

Use technology to compute BA and AB if

2 4 11 2

3 2 10 1 and

2 0 23 2

1 3 0

A B

Assignment

Pg. 531-535#1-9 all#14-15#17-20all#27-28#34 and #39