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A matrix is a rectangular array of numbers or symbols used in various fields to represent and solve systems of linear equations, perform transformations, and organize data. Basic operations on matrices include addition, subtraction, scalar multiplication, matrix multiplication, and transposition. Matrices are widely applied in solving linear equations, graph theory, computer graphics, and data science.

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16 views2 pages

Concise Document

A matrix is a rectangular array of numbers or symbols used in various fields to represent and solve systems of linear equations, perform transformations, and organize data. Basic operations on matrices include addition, subtraction, scalar multiplication, matrix multiplication, and transposition. Matrices are widely applied in solving linear equations, graph theory, computer graphics, and data science.

Uploaded by

EricXIze
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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INTRODUCTION TO MATRICES

A matrix is a rectangular array of numbers, symbols, or expressions arranged


in rows and columns. Matrices are widely used in various fields such as
mathematics, physics, computer science, and engineering to represent and
solve systems of linear equations, perform transformations, and organize
data efficiently.

BASIC CONCEPTS
A matrix is typically denoted by a capital letter, for example, A, and its
elements are written as aij, where i indicates the row number and j the
column number.

For example, a 2x3 matrix A looks like this:

A = \begin{bmatrix}
a_{11} & a_{12} & a_{13} \\
a_{21} & a_{22} & a_{23}
\end{bmatrix}

MATRIX OPERATIONS
Matrices support several basic operations including:

• Addition and Subtraction: Matrices of the same size can be added or


subtracted element-wise.
• Scalar Multiplication: Every element of a matrix is multiplied by a scalar
(a single number).
• Matrix Multiplication: The product of an m × n matrix and an n × p
matrix is an m × p matrix, computed via the dot product of rows and
columns.
• Transpose: Flipping a matrix over its diagonal, switching the row and
column indices.
APPLICATIONS OF MATRICES
Matrices are essential in many applications such as:

• Solving systems of linear equations using methods like Gaussian


elimination.
• Graph theory and networks representation.
• Computer graphics for transforming shapes and coordinates.
• Data science for handling datasets arranged in tabular form.

In summary, matrices provide a structured way to organize numerical data


and apply mathematical techniques to analyze and manipulate that data
effectively.

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