Chapter Nine — Matrix Operations and Calculations

The Humongous Book of Algebra Problems

182

Anatomy of a Matrix

The order of a matrix and identifying elements

Note: Problems 9.1–9.3 refer to matrix A deﬁned below and the elements a

ij

of matrix A.

9.1 What is the order of the matrix?

Order indicates the dimensions—the number of rows and columns—of a

matrix. Matrix A has two horizontal rows and ﬁve vertical columns, so it has

order 2 × 5. Note that order is always written r × c, where r is the number of rows

and c is the number of columns.

Note: Problems 9.1–9.3 refer to matrix A deﬁned below and the elements a

ij

of matrix A.

9.2 Identify element a

13

.

The individual numbers within a matrix are called elements and are labeled

using the notation a

ij

. Element a

ij

is in the ith row and the jth column of matrix

A. Element a

13

is in the ﬁrst row and the third column from the left: a

13

= –3.

Note: Problems 9.1–9.3 refer to matrix A deﬁned below and the elements a

ij

of matrix A.

9.3 Identify element a

21

.

As explained in Problem 9.2, the notation a

21

describes the element in the

second row (from the top) and ﬁrst column (from the left): a

21

= 0.

The i and

j here represent

numbers: a

11

and

a

23

represent specic

positions in the matrix,

as you’ll see in

Problems 9.2–9.3

and 9.5–9.6.

The rst

number always

tells you how many

rows are in the

matrix, and the

second value always

represents the

number of

columns.

The rst

number (i)

tells you what

horizontal row the

element is in (1 =

top row, 2 = second

row from the top, and

so on), and the second

number (j) tells you

what vertical column

the number is in (1 =

far left column, 2 =

second column

from the left,

and so on).

Matrices are labeled with capital

letters and elements of matrices are labeled

with lowercase versions of the same letters. Elements

of matrix A look like a

21

and elements of matrix B

look like b

21

.

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