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Matrix Multiplication

- Section 4-3
- Algebra II CP
- Mrs. Sweet

Row by Column Multiplication

- The product of matrix A and B is found by

multiplying the of matrix A by the of

matrix B. - Then the final products.

row

column

adding

12

-3

19

10

Matrices can be multiplied only when the number

of for the left matrix matches the number

of of the right matrix.

columns

rows

If A has dimensions n x p and B has dimensions

p x q then AB will have dimensions

n x q

A is a 3 x 5 B is a 2 x 5 C is a 5 x 1 D

is a 3 x 2

Examples 1) Given the dimensions of the

following matrices determine if they can be

multiplied if so find the dimensions of their

product

A is a 3 x 5 B is a 2 x 5 C is a 5 x

1 D is a 3 x 2

Is matrix multiplication Commutative?

Give an example

Is matrix multiplication Associastive?

Give an example

2) Find the product of the given matrices

2) Find the product of the given matrices

6 2

5 -4

8 1

2 0

0 3

22

50

12

-12

3

0

An ounce of ground beef has about 60 calories. A

single French fry has about 11 calories. An

ounce of yogurt has about 40 calories. 1) If

you eat a quarter pound of beef, 20 French fries,

and 4 ounces of yogurt, how many calories will

you have consumed? 2) Write the question as

a matrix multiplication.

Identity Matrix Find the product of I and A

An Identity Matrix is an n x n matrix whose

main from upper left to lower right

has all elements 1 while all other elements are 0.

diagonal

What would be the identity matrix for a 3 x 3

matrix?

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