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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 dimensionsthe number of rows and columnsof 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 specic
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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