Download Algebra 2 Organizing Data Into Matrices

Organizing Data Into Matrices
Lesson 4-1
Algebra 2
Organizing Data Into Matrices
Algebra 2
Matrix- a rectangular array of numbers written within brackets.
Matrix Element- each number in a matrix.
Organizing Data Into Matrices
Lesson 4-1
Algebra 2
Additional Examples
Write the dimensions of each matrix.
a.
7 –4
12 9
The matrix has 2 rows and 2 columns and is
b.
0 6 15
The matrix has 1 row and 3 columns and is
therefore a 2  2 matrix.
therefore a 1  3 matrix.
Algebra 2
Matrix Element- each number in a matrix.
Organizing Data Into Matrices
Lesson 4-1
Algebra 2
Additional Examples
Identify each matrix element.
K =
3 –1 –8 5
1 8 4 9
8 –4 7 –5
a. k12
a. K =
b. k32
3 –1 –8 5
1 8 4 9
8 –4 7 –5
c. k23
b. K =
d. k34
3 –1 –8 5
1 8 4 9
8 –4 7 –5
k12 is the element in the first row
and second column.
k32 is the element in the third row
and second column.
Element k12 is –1.
Element k32 is –4.
Organizing Data Into Matrices
Lesson 4-1
Algebra 2
Additional Examples
(continued)
K =
3 –1 –8 5
1 8 4 9
8 –4 7 –5
a. k12
c. K =
b. k32
3 –1 –8 5
1 8 4 9
8 –4 7 –5
c. k23
d. K =
d. k34
3 –1 –8 5
1 8 4 9
8 –4 7 –5
k23 is the element in the second
row and third column.
k34 is the element in the third row
and the fourth column.
Element k23 is 4.
Element k34 is –5.
Organizing Data Into Matrices
Lesson 4-1
Algebra 2
Additional Examples
Three students kept track of the games they won and lost in
a chess competition. They showed their results in a chart. Write a
2

3 matrix to show the data.
= Win
Ed
X = Loss
X
X
Jo
Lew
X
X
X X
X
Let each row represent the number of wins and losses and each
column represent a student.
Ed Jo Lew
Wins
Losses
5
2
6
1
3
4
Organizing Data Into Matrices
Lesson 4-1
Algebra 2
Additional Examples
Refer to the table.
a. Write a matrix N to represent
the information.
Use 2  3 matrix.
U.S. Passenger Car Imports
And Exports (millions)
1996
1998
2000
Imports
4.678
5.185
6.964
Exports
1.295
1.331
1.402
Source: U.S. Department of Commerce.
Each column represents a
different year.
N = Import
Exports
1996
1998
2000
4.678
1.295
5.185
1.331
6.964
1.402
Each row represents
imports and exports.
Organizing Data Into Matrices
Lesson 4-1
Algebra 2
Additional Examples
(continued)
b. Which element represents
exports for 2000?
U.S. Passenger Car Imports
And Exports (millions)
1996
1998
2000
Imports
4.678
5.185
6.964
Exports
1.295
1.331
1.402
Source: U.S. Department of Commerce.
Exports are in the second row.
The year 2000 is in the third column.
Element n23 represents the number of exports for 2000.
Organizing Data Into Matrices
Algebra 2
8
1. Write the dimensions of the matrix. M = 9
–1
4 0
3 –5
2 6
1
0
1
2. Identify the elements m24, m32, and m13 of the matrix M in question 1.
3. The table shows the amounts of the deposits and withdrawals for the
checking accounts of four bank customers. Show the data in a 2  4
matrix. Label the rows and columns.
Deposits Withdrawals
A
$450
$370
B
$475
$289
C
D
$364
$420
$118
$400
Organizing Data Into Matrices
Algebra 2