Scribd
Upload
108 views1 page

Matrices 5

- Vectors are matrices with a single row or column. They are represented by lowercase bold letters and their components are indexed in brackets. - Matrices and vectors can undergo addition and scalar multiplication, which allows them to be used in computations like numbers. - Two matrices are equal if and only if they are the same size and have equal corresponding entries. Matrices of different sizes are always different.

Uploaded by

smile km
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
108 views1 page

Matrices 5

- Vectors are matrices with a single row or column. They are represented by lowercase bold letters and their components are indexed in brackets. - Matrices and vectors can undergo addition and scalar multiplication, which allows them to be used in computations like numbers. - Two matrices are equal if and only if they are the same size and have equal corresponding entries. Matrices of different sizes are always different.

Uploaded by

smile km
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 1

SEC. 7.

1 Matrices, Vectors: Addition and Scalar Multiplication 259

Vectors
A vector is a matrix with only one row or column. Its entries are called the components
of the vector. We shall denote vectors by lowercase boldface letters a, b, Á or by its
general component in brackets, a 3aj4, and so on. Our special vectors in (1) suggest
that a (general) row vector is of the form

a 3a1 a2 Á an4. For instance, a 3 2 5 0.8 0 14.

A column vector is of the form

b1
4
b2
b . . For instance, b 0 .
.
. 7
bm

Addition and Scalar Multiplication


of Matrices and Vectors
What makes matrices and vectors really useful and particularly suitable for computers is
the fact that we can calculate with them almost as easily as with numbers. Indeed, we
now introduce rules for addition and for scalar multiplication (multiplication by numbers)
that were suggested by practical applications. (Multiplication of matrices by matrices
follows in the next section.) We first need the concept of equality.

DEFINITION Equality of Matrices


Two matrices A 3ajk4 and B 3bjk4 are equal, written A B, if and only if
they have the same size and the corresponding entries are equal, that is, a11 b11,
a12 b12, and so on. Matrices that are not equal are called different. Thus, matrices
of different sizes are always different.

EXAMPLE 3 Equality of Matrices


Let

a11 a12 4 0
A c d and B c d.
a21 a22 3 1

Then

a11 4, a12 0,
A B if and only if
a21 3, a22 1.

The following matrices are all different. Explain!

1 3 4 2 4 1 1 3 0 0 1 3
c d c d c d c d c d
4 2 1 3 2 3 4 2 0 0 4 2

You might also like