<< Chapter < Page Chapter >> Page >
In this section, you will:
  • Find the sum and difference of two matrices.
  • Find scalar multiples of a matrix.
  • Find the product of two matrices.
(credit: “SD Dirk,” Flickr)

Two club soccer teams, the Wildcats and the Mud Cats, are hoping to obtain new equipment for an upcoming season. [link] shows the needs of both teams.

Wildcats Mud Cats
Goals 6 10
Balls 30 24
Jerseys 14 20

A goal costs $300; a ball costs $10; and a jersey costs $30. How can we find the total cost for the equipment needed for each team? In this section, we discover a method in which the data in the soccer equipment table can be displayed and used for calculating other information. Then, we will be able to calculate the cost of the equipment.

Finding the sum and difference of two matrices

To solve a problem like the one described for the soccer teams, we can use a matrix    , which is a rectangular array of numbers. A row    in a matrix is a set of numbers that are aligned horizontally. A column    in a matrix is a set of numbers that are aligned vertically. Each number is an entry    , sometimes called an element, of the matrix. Matrices (plural) are enclosed in [ ] or ( ), and are usually named with capital letters. For example, three matrices named A , B , and C are shown below.

A = [ 1 2 3 4 ] , B = [ 1 2 7 0 −5 6 7 8 2 ] , C = [ −1 0 3 3 2 1 ]

Describing matrices

A matrix is often referred to by its size or dimensions:   m   ×   n   indicating m rows and n columns. Matrix entries are defined first by row and then by column. For example, to locate the entry in matrix A identified as a i j , we look for the entry in row i , column j . In matrix A ,   shown below, the entry in row 2, column 3 is a 23 .

A = [ a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 ]

A square matrix is a matrix with dimensions   n   ×   n , meaning that it has the same number of rows as columns. The 3 × 3 matrix above is an example of a square matrix.

A row matrix is a matrix consisting of one row with dimensions 1   ×   n .

[ a 11 a 12 a 13 ]

A column matrix is a matrix consisting of one column with dimensions m   ×   1.

[ a 11 a 21 a 31 ]

A matrix may be used to represent a system of equations. In these cases, the numbers represent the coefficients of the variables in the system. Matrices often make solving systems of equations easier because they are not encumbered with variables. We will investigate this idea further in the next section, but first we will look at basic matrix operations .

Matrices

A matrix    is a rectangular array of numbers that is usually named by a capital letter: A , B , C , and so on. Each entry in a matrix is referred to as a i j , such that i represents the row and j represents the column. Matrices are often referred to by their dimensions: m × n indicating m rows and n columns.

Finding the dimensions of the given matrix and locating entries

Given matrix A :

  1. What are the dimensions of matrix A ?
  2. What are the entries at a 31 and a 22 ?
    A = [ 2 1 0 2 4 7 3 1 2 ]
  1. The dimensions are   3   ×   3   because there are three rows and three columns.
  2. Entry a 31 is the number at row 3, column 1, which is 3. The entry a 22 is the number at row 2, column 2, which is 4. Remember, the row comes first, then the column.
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Questions & Answers

how do I set up the problem?
Harshika Reply
what is a solution set?
Harshika
find the subring of gaussian integers?
Rofiqul
hello, I am happy to help!
Shirley Reply
please can go further on polynomials quadratic
Abdullahi
I need quadratic equation link to Alpa Beta
Abdullahi Reply
find the value of 2x=32
Felix Reply
divide by 2 on each side of the equal sign to solve for x
corri
X=16
Michael
Want to review on complex number 1.What are complex number 2.How to solve complex number problems.
Beyan
use the y -intercept and slope to sketch the graph of the equation y=6x
Only Reply
how do we prove the quadratic formular
Seidu Reply
hello, if you have a question about Algebra 2. I may be able to help. I am an Algebra 2 Teacher
Shirley Reply
thank you help me with how to prove the quadratic equation
Seidu
may God blessed u for that. Please I want u to help me in sets.
Opoku
what is math number
Tric Reply
4
Trista
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
Sidiki Reply
Need help solving this problem (2/7)^-2
Simone Reply
x+2y-z=7
Sidiki
what is the coefficient of -4×
Mehri Reply
-1
Shedrak
the operation * is x * y =x + y/ 1+(x × y) show if the operation is commutative if x × y is not equal to -1
Alfred Reply
An investment account was opened with an initial deposit of $9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
Kala Reply
lim x to infinity e^1-e^-1/log(1+x)
given eccentricity and a point find the equiation
Moses Reply
Practice Key Terms 5

Get the best College algebra course in your pocket!





Source:  OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College algebra' conversation and receive update notifications?

Ask