INTRODUCTION TO MATRICES

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A MATRIX (pronounced MAY-trix) is a rectangular arrangement of numbers, like [ 7 3 2 6 5 8 ] .
A number in a matrix is often called an element, a member, or an entry of the matrix.
The members of a matrix are enclosed in (square) brackets.

ROWS have a horizontal orientation, and are numbered from top to bottom:

7	3	2

6	5	8

Thus, [ 7 3 2 ] is the first row, and [ 6 5 8 ] is the second row.

COLUMNS have a vertical orientation, and are numbered from left to right:

7		3		2
6		5		8

Thus, [ 7 6 ] is the first column, [ 3 5 ] is the second column, and [ 2 8 ] is the third column.

The plural of matrix is MATRICES (pronounced MAY-tri-sees).

Matrices offer a way to represent large amounts of data in an organized way.
Matrices are particularly well-suited to computer analysis.
There are a multitude of applications of matrices, including:

encrypting numerical data (think national security)
computer graphics (think video games)
solving systems of equations

The size of a matrix is reported by stating the number of rows, followed by the number of columns.
For example, the size of [ 7 3 2 6 5 8 ] is 2×3 , which is read aloud as 2 by 3 .
Observe that an m×n matrix has mn elements.

Matrices are usually named with capital letters.
Members of a matrix are usually named with lowercase letters.
In particular, the elements of a matrix M are conventionally named mij :

mij is read aloud as "m sub i j"
the i and j are called subscripts; they are written a little bit below the line
the first subscript ( i ) gives the row number of the element
the second subscript ( j ) gives the column number of the element
a capital letter is used to denote the matrix, and the corresponding lowercase letter is used to denote the elements

For example, if M= [ 7 3 2 6 5 8 ] , then:
m11=7   (first row, first column; read as em sub one one, NOT (say) em sub eleven)
m12=3   (first row, second column)
m13=2   (first row, third column)
m21=6   (second row, first column)
m22=5   (second row, second column)
m23=8   (second row, third column)

Two matrices are equal precisely when they have the same size, and corresponding elements are equal.
Precisely, we have:

EQUALITY OF MATRICES

Let A and B be matrices.
Then,

A=B

if and only if

A and B have the same size
and
aij =bij for all i and j .

Here, i takes on all possible row numbers, and j takes on all possible column numbers.

A matrix with the same number of rows and columns is called a square matrix .
A matrix where all the entries are zero is called a zero matrix .

On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.

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