Matrices The Basics

1
Matrices The Basics

• Vocabulary and basic concepts

2
A matrix is an array of numbers For example Three
classes are split into boys and girls. A 15 boys
and 17 girls. B 18 boys and 14 girls. C 10 boys
and 19 girls. This data could be arranged as a 2
X 3 MATRIX.
3
A matrix with R rows and C columns is called an R
X C Matrix. This is called the ORDER of the
matrix. Each entry in the matrix is called an
ELEMENT.
4
The CO-ORDINATE (2,3) has ONE ROW and TWO
COLUMMS. It is a 1X2 matrix A matrix with only
one row is called a ROW VECTOR. The vector
represents a TRANSLATION or shift 6 units to
the right and 2 units down. A matrix with only
one column and any number of rows is called a
COLUMN VECTOR.
A Matrix with the same number of ROWS as COLUMNS
is called a SQUARE MATRIX.
5
Addition and Subtraction of Matrices
We may add or subtract two matrices ONLY if they
have the SAME ORDER.
Adding or subtracting matrices is carried out by
adding or subtracting their corresponding
elements.
If two matrices A and B are of UNEQUAL ORDER
then A B does not exist.
6
Addition and Subtraction of Matrices
If two matrices A and B are of EQUAL ORDER then
A B B A Addition of Matrices (where
allowed) is COMMUTATIVE
7
EQUAL MATRICES
Two matrices A and B are equal if EVERY element
in A is equal to EVERY element in B. Two
matrices may be the SAME ORDER but NOT EQUAL.
CAN YOU SEE WHY?
8
Multiplication by a Scalar
If k is a constant scalar, the matrix kA is such
that EACH OF ITS ENTRIES ARE MULTIPLIED by k
9
The ZERO or NULL Matrix
Has every element ZERO.
Adding or subtracting the NULL Matrix will have
no effect.
MULTIPLYING by the NULL Matrix will create
another NULL MATRIX.
10
The UNIT or IDENTITY MATRIX I
A VERY IMPORTANT MATRIX. (Later work!)
These are always SQUARE MATRICES
This is denoted by the letter I and has zero
entries except for 1s on the diagonal.
MULTIPLYING by the IDENTITY Matrix will create
the SAME MATRIX. In a similar way to Multiplying
a number by 1
11
The TRANSPOSE OF A MATRIX
The rows are written as columns and the columns
as rows.