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I can write matrix dimension, identify elements in a matrix, and add/subtract/solve matrices.
4.1: Organizing Data into Matrices
Matrix: (plural is matrices) is a rectangular array of numbers written in brackets.
 You represent a matrix with a capital letter and its dimensions. The number of horizontal rows by the
number of vertical columns determines the dimensions. (HR x VC)
−4 7
If = [ 9 −9] , the matrix A is a _______________ matrix.
−9 1
Example: Write the dimensions of each of the following matrices.
4
[2
1
6
5
−3 −7]
0
9
[−4
1
3
1
[2]
0
0.5
−3]
Matrix Elements: each number in a matrix.
 Each element is represented with a lower case letter with subscripts.
 The subscripts represent the element’s row number and column number.
o The first number of the subscript is the row number, and the second number is the column
number.
𝑎11
𝐴 = [𝑎21
𝑎31
𝑎12
𝑎22
𝑎32
𝑎13
𝑎23 ]
𝑎33
Example: Identify each Matrix element.
2
4
If = [−8 −1] , then 𝑎22 = _____ , 𝑎31 = _____ , and 𝑎12 = _____ .
3
5
Example: Energy is often measured in British thermal unit (Btus). Write a matrix to represent the data below.
(See image on page 165 of the textbook!)
China
Russia
United States
Production
33
41
73
Consumption
34
26
95
4.2: Adding and Subtracting Matrices
Matrix Addition and Subtraction: Matrices must be of EQUAL DIMENSION.
 Add or subtract elements in corresponding positions.
I can write matrix dimension, identify elements in a matrix, and add/subtract/solve matrices.
Example: Find the sum or difference of the following matrices.
[
5 7 9
−5 −5 4
]+[
]
−9 1 −3
−3 −6 2
[
−3 2
9 6
]−[
]
−2 1
7 −4
Identity and Inverse Matrices: JUST LIKE WITH REAL NUMBERS!!!
 ZERO Matrix: a matrix whose elements are all zeros. (This is also known as the IDENTITY matrix.)
[

2 3
0
]+[
2 8
0
0
]=
0
Additive Inverse Matrix: the opposite matrix (or additive inverse matrix) of a m x n matrix A is –A.
o All of the elements in –A have opposite signs of those in original matrix A.
o –A is the matrix that would make 𝐴 + −𝐴 = 𝑖𝑑𝑒𝑛𝑡𝑖𝑡𝑦 𝑚𝑎𝑡𝑟𝑖𝑥. (or zero matrix)
1
9 2
−1 −9 −2
1
9 2
−1
If = [
] , then – 𝐴 = [
] and [
]+[
−3 −1 7
3
1 −7
−3 −1 7
3
−9 −2
]=
1 −7
Solving Matrix Equations:
 Matrix Equations: equation in which the variable is a matrix. You can you the addition and subtraction
properties of equality to solve matrix equations.
Example: Solve 𝑋 − [

1 1
0 1
]=[
] for the matrix X.
3 2
8 9
Equal Matrices: matrices with the SAME dimensions and EQUAL corresponding elements.
Example: Determine whether or not the following matrices are equal.
−0.75
𝐴=[ 1
2

1
−3
0.2
] 𝑎𝑛𝑑 𝐵 = [ 4
]
−2
0.5 −2
5
Finding Unknown Matrix Elements: Solve the equations by setting corresponding elements equal to
each other.
Example: Solve the equation(s) for x and y. What are the missing elements?
[
2𝑥 − 5
4
25
]=[
3
3𝑦 + 12
3
4
]
𝑦 + 18