Organizing Data Into Matrices
Objective: to identify matrices and thier elements and organize data into matrices.
Title: Aug 27­12:54 PM (1 of 8)
Check your skills!
How many units were importaed in 1996?
Unided States passenger vehicles and light trucks imports and exports in millions.
1996
1998
2000
How many more units were imported in 1998 than in 1996?
How many more units were imported than exported in 2000?
Compare the percent increase of imports to the percent increase of exports from 1996 to 2000.
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imports 4.678 5.185 6.964
exports 1.295 1.331 1.402
Definition: Matrix (Plural : Matrices) Is a rectangular array of numbers written within brackets. You represent a matrix with a capital letter and classify it by its dimensions. The number of horizontal rows and the number of vertical columns determine the dimensions of a matrix.
3 columns
A =
2 3 4
6 7 0
Matrix A is a 2 x 3 matrix.
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2 rows Example 1
4 6 5
a.
2 ­3 ­7
1 0 9
3 row x 3 columns
3 x 3
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b.
­4 1/3 ­3
1 row x 3 columns
1 x 3 c.
1
2
0
0.5
4 row x 1 columns
4 x 1
Definition: Matrix Element Each number in a matrix is a matrix element. You can identify a matrix element by its position within the matrix. Use a lowercase latter with subscripts. THe subscripts represent the element's row and column number.
Identify element a13 in matrix A below
A =
17 24 3
10.4 12 15
6 30 15
Element a13 is 3
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a13 is the element in the first row and thrid column
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Example 2
A =
17 24 3
10.4 12 15
6 30 15
Identify each matrix element.
a. a33
b. a11
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c. a 21
d. a12
Example 3
Write a matrix to to represeint the data below.
China
Production
Consumption
Russia
United States
40
20
0
60
80
100
Energy (1015 BTU)
Production Consumption
China
42 43
Russia
46 28
United States
71
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98
Can you write the matrix as a 2 x 3 matrix? Label your rows and columns.
Example 4
Gymnast
Floor Exercise Vault Balance Beam Uneven Bars
M. Bhardwaj 9.525 9.337 9.350 9.487
C. Kupets
9.400 9.350 9.550 9.637
C. McCool
9.250 9.350 9.112 9.575
C. Patterson
9.500 9.512 9.725 9.600
Write a matrix W to represent the information. Use a 4 x 4 matrix.
W =
Floor Exercise Vault Balance Beam Uneven Bars
M. Bhardwaj 9.525 9.337 9.350 9.487
C. Kupets
9.400 9.350 9.550 9.637
C. McCool
9.250 9.350 9.112 9.575
C. Patterson
9.500 9.512 9.725 9.600
Which element represents C. McCool score on the vault?
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Title: Aug 27­12:54 PM (8 of 8)