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Ch.4, Lesson 3, Objective 2 Page 1 of 5
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Algebra 2 Home
Page go
Matrix Multiplication
Chapter 4
Matrices
4-1 Organizing Data
Into Matrices
4-2 Adding and Multiplying Matrices
Subtracting Matrices
4-3 Matrix
Multiplication
Objective 1
Objective 2
Exercises Investigation: Using Mat
Checkpoint
Quiz 1
Use the data in the table.
4-4 Geometric
Transformations With
Matrices
4-5 2 x 2 Matrices,
Determinants, and
Inverses
4-6 3 x 3 Matrices,
Determinants, and
Inverses 1. How much money did the cafeteria collect sellin
4-7 Inverse Matrices 1? Selling lunch 2? Selling lunch 3?
and Systems
4-8 Augmented 2.
Matrices and Systems
a. How much did the cafeteria collect sellin
Assessment
three lunches?
Real-World Snapshots
b. Explain how you used the data in the ta
find your answer.
3.
a. Write a 1 × 3 matrix to represent the co
the lunches.
b. Write a 3 × 1 matrix to represent the n
of lunches sold.
c. Writing Describe a procedure for using
matrices to find how much money the caf
collected from selling all three lunches. U
words row, column, and element.
To perform t i lti li ti m ltipl the elements o
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Ch.4, Lesson 3, Objective 2 Page 2 of 5
To perform matrix multiplication, multiply the elements o
each row of the first matrix by the elements of each column
You can use the the second matrix. Add the products.
MATRX feature of a
graphing calculator
to multiply
matrices.
Multiplying Matrices
Find the product of and .
Multiply a 11 and b 11 . Then multiply a 12 and b 21 . Add
products.
The result is the element in the first row and first colum
Repeat with the rest of the rows and columns.
The product of and is .
Check Understanding
Definition Matrix Multiplication
To find element c ij of the product matrix AB, multiply ea
element in the ith row of A by the corresponding elemen
column of B, and then add.
You can use matrix multiplication to solve problems.
Real-World Connectio
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Ch.4, Lesson 3, Objective 2 Page 3 of 5
Business A used-record store sells tapes, LP record
compact discs. The matrices show today's information
store's gross income for the day.
Recording
Play Video
(5.1 MB)
The music on an LP
record plays
continuously as the
stylus travels along
the groove. The Multiply each price by the number of items sold and a
music on a CD plays products.
in discrete intervals
read by a laser.
The store's gross income for the day was $512.
Check Understanding
The product of two matrices A and B exists only if the numb
columns of A is equal to the number of rows of B.
Property Dimensions of a Product Mat
If matrix A is an m × n matrix and matrix B is an n × p
then the product matrix AB is an m × p matrix.
The dimensions of product matrix AB is 3 × 4.
Determining Whether a Pr
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Ch.4, Lesson 3, Objective 2 Page 4 of 5
Use matrices G = and H = . Determine w
products GH and HG are defined (exist) or undefined (
exist).
Find the dimensions of each product matrix.
Product GH is defined and is a 3 × 2 matrix. Product H
undefined, because the number of columns of H is not
the number of rows of G.
Check Understanding
Matrix multiplication has some of the properties of real num
multiplication.
Properties Matrix Multiplication
If A, B, and C are n × n matrices, then
Exercises Click here to view the Exercises for this less
Checkpoint Quiz 1
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Ch.4, Lesson 3, Objective 2 Page 5 of 5
Ch apt er 4: Matr ice s, Le s so n 4 -3 ( 18 0 –182 )
Pre nt ice Hall Math emat ics Al gebra 2 iTex t
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