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Matrix Operations. Chapter 4: Matrices Lesson 1: using Matrices to Represent Data. Objectives: Represent mathematical and real-world data in a matrix. Find sums and differences of matrices and the scalar product of a number and a matrix. - PowerPoint PPT Presentation
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Chapter 4: MatricesChapter 4: MatricesLesson 1: using Matrices to Represent Lesson 1: using Matrices to Represent
DataData
Objectives:Objectives:– Represent mathematical and real-world data in Represent mathematical and real-world data in
a matrix.a matrix.– Find sums and differences of matrices and the Find sums and differences of matrices and the
scalar product of a number and a matrix.scalar product of a number and a matrix.
MATRIX:MATRIX: A rectangular A rectangular arrangement of arrangement of numbers in rows and numbers in rows and columns.columns.
The The ORDERORDER of a matrix of a matrix is the number of the is the number of the rows and columns.rows and columns.
The The ENTRIESENTRIES are the are the numbers in the matrix.numbers in the matrix.
502
126rows
columns
This order of this matrix This order of this matrix is a 2 x 3.is a 2 x 3.
67237
89511
36402
3410
200
318 0759
20
11
6
0
7
9
3 x 3
3 x 5
2 x 2 4 x 1
1 x 4
(or square matrix)
(Also called a row matrix)
(or square matrix)
(Also called a column matrix)
To add two matrices, they must have the same To add two matrices, they must have the same order. To add, you simply add corresponding order. To add, you simply add corresponding entries.entries.
34
03
12
70
43
35
)3(740
0433
13)2(5
44
40
23
9245
3108
2335
2571
)1(8 70 51 23
55 34 32 )2(9 =
= 7 7 4 5
0 7 5 7
To subtract two matrices, they must have the same To subtract two matrices, they must have the same order. You simply subtract corresponding entries.order. You simply subtract corresponding entries.
232
451
704
831
605
429
2833)2(1
)4(65015
740249
603
1054
325
724
113
810
051
708
342
=
5-2
-4-1 3-8
8-3 0-(-1) -7-1
1-(-4)
2-0
0-7
=
2 -5 -5
5 1 -8
5 3 -7
In matrix algebra, a real number is often called a In matrix algebra, a real number is often called a SCALARSCALAR. . To multiply a matrix by a scalar, you multiply each entry in To multiply a matrix by a scalar, you multiply each entry in the matrix by that scalar. the matrix by that scalar.
14
024
416
08
)1(4)4(4
)0(4)2(4
86
54
30
212
)8(360
52412
-2
6
-3 3
-2(-3)
-5
-2(6) -2(-5)
-2(3) 6 -6
-12 10
Assignment 1Assignment 1
• Ch.4.1 pg.221 # 6 to 9, 12 to 14, Ch.4.1 pg.221 # 6 to 9, 12 to 14, and 19 to 23.and 19 to 23.
•Due date: Sept. 30Due date: Sept. 30thth, 2009, 2009
•To: Mr. Mohammed AkourTo: Mr. Mohammed Akour
•By email: By email: [email protected] [email protected]
This presentation edited by Mr. Mohammed AkourMr Wassim Fakih
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