1.1 Matrices
Learning Goal: In this lesson you will learn about matrices, equal
matrices, and operations with matrices.
Matrices
A matrix is a rectangular array of numbers used to manage and
organize data.
For example, a mathematics teacher records grade information
for two sections of a mathematics course in the following matrix:
Each row represents a different type of grade, and each column
represents a section.
Each number appearing in the matrix is called an entry.
Practice 1
Summarize the given information in matrix form.
1. An appliance saleswoman sold 15 washers, 8 dryers, and 13
microwave ovens in March. She sold 12 washers, 11 dryers, and
6 microwave ovens in April.
2. Tom scored 78, 82, and 72 on the first three biology exams. John
scored 62, 71, and 76. Harriet scored 98, 70, and 81.
Matrices
Matrices
For example,
is a 2 x 3 matrix because it has two rows and three columns and
is a 4 x 3 matrix, having four rows and three columns.
Practice 2
State the size of each matrix and the entries.
1.
2.
Matrices
Find a square matrix 𝐴 such that the dimension is 3 x 3 and aij = 2i + j
Practice 3
Find a matrix 𝐴 such that the dimension is 2 x 3 and aij = ( i + 1)
j
Transpose Matrix
The transpose matrix 𝐴𝑇 of a matrix A is obtained by interchanging
the rows and columns.
For example:
if
 −1 3 
A =  0 5 
 2 −4 
then
 −1 0 2 
A =

3
5
−
4


T
Practice 4
Find 𝐴𝑇 if
 5 1 −3
1. A = 

−
2
0
1


 2 0 −4 


2. A =  1 6 3 
 −5 0 1 
Equal Matrices
For example
if
then 𝑎 = 1, 𝑏 = 3, 𝑐 = 5, and 𝑑 = 2.
Equal Matrices
2. Find the value of 𝑥 that makes the pairs of matrices equal.
3. Find the value of 𝑥 and 𝑦 that makes the pairs of matrices
equal.
Practice 5
1 
 x 2 − 1 1 8
Find 𝑥, 𝑦, and 𝑧 if 
=

7
−
3
z
−
7
2
y
+
3
5




Operations With Matrices
Operations With Matrices
Let
Carry out each indicated operation or explain why it cannot be
performed.
𝐚) 𝐴 + 𝐵
b) C – D
c) 𝐶 + 𝐴
d) 5A
Operations With Matrices
a) A + B =
b) C – D =
c) C + A
d) 5A =
is undefined because we can’t add matrices of
different dimensions.
Practice 6
Homework
Page 60 #1, 2, 6, 7, 8, 13