Download - Matrix basic operations
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
Matrix MultiplicationMatrix Multiplication
Matrix Multiplication is NOT Matrix Multiplication is NOT Commutative! Order matters!Commutative! Order matters!
You can multiply matrices You can multiply matrices onlyonly if the if the number of number of columnscolumns in the first matrix in the first matrix equals the number of equals the number of rowsrows in the second in the second matrix.matrix.
2 3
5 6
9 7
2 columns2 rows
1 2 0
3 4 5
Matrix MultiplicationMatrix Multiplication
Take the numbers in the first row of Take the numbers in the first row of matrix #1. Multiply each number by its matrix #1. Multiply each number by its corresponding number in the first column corresponding number in the first column of matrix #2. Total these products.of matrix #2. Total these products.
2 3
5 6
9 7
1 2 0
3 4 5
21 33 11
The result, 11, goes in row 1, column 1 of the answer. Repeat with row 1, column 2; row 1 column 3; row 2, column 1; ...
Matrix MultiplicationMatrix Multiplication
Notice the dimensions of the matrices and Notice the dimensions of the matrices and their product.their product.
2 3
5 6
9 7
1 2 0
3 4 5
11 8 15
13 34 30
12 46 35
3 x 2 2 x 3 3 x 3__ __ __ __
Matrix MultiplicationMatrix Multiplication
Another example:Another example:
2 15
9 02
10 5
3 x 2 2 x 1 3 x 1
8
45
60