Download Lesson 12-1

Notes for Lesson 12 – 1: Organizing Data Using Matrices
Vocabulary:
Matrix – A rectangular arrangement of numbers in rows and columns
Element – Each number in a matrix
Scalar – A real number used for multiplying a matrix
Scalar Multiplication – An operation that multiplies a matrix by a scalar
A matrix is a rectangular arrangement of data in rows and columns. You identify the size of a matrix by the
number of row and the number of columns.
So for the following matrix it would be a 3 x 2 because it has 3 rows and 2 columns.
5 1
2 0
3 4
Matrices are used to organize data and make it easier to perform calculations on the data
12-1.1 – Adding and subtracting matrices
You may need to add or subtract matrices in order to solve problems. You can only add or subtract matrices
that are the same size. You then add or subtract the matrices by adding or subtracting corresponding elements.
Examples:
−8 −1.2
−5 2.7
−3 −3.9
[
]+[
]=[
]
3
−1
−4
2
7 −3
2 11
−1
8
3
3
[−4 3.2] − [−6.5 4 ] = [2.5 −0.8]
1.5 −5
0
−3
1.5 −2
12.1-2 – Multiplying a matrix by a scalar
You may also need to multiply a matrix by a real number in order to solve a problem. The real number
multiplier is called a scalar. Multiplying a matrix by this scalar is called scalar multiplication. To multiply a
matrix by a scalar, distribute the scalar to each element in the matrix.
Examples:
3[
4 −1.5
12
]=[
1 −6
3
−4.5
]
−18
4 0
−2 [
−2 1
−8 0
5
]=[
4 −2
2
−10
]
−4
If you have a combination of multiplication and addition/subtraction remember in the order of operations that
multiplication comes first.
3 0
6
0
6 −5
6 −5
0
[0
3 ] − 2 [−1 4] = [ 0
3 ] − [ −2 8] = [ 2
−6 2
−12 4
10
−2 1
−2 1
−5
−5]
−3
12.1-3 – Using Matrices
Which city has the greatest average number of clear days in a full year?
Sept-Feb
Clear Cloudy
102 41
[ 43 58] +
55 82
March-Aug
Total
Clear Cloudy
110 27
[ 31 59]
=
45 83
Clear Cloudy
212 68
[ 74 117]
100 165
So, Phoenix has the most clear days with 212. Portland the most cloudy with 165.
892 351
739 215
153 136
46 ] so 166 more students played soccer among students.
⌈1114 483⌉ − [1023 437] = [ 91
−37 6
653 64
690 58
166 −5
1712 37
1546 42