Fundamental concept in matrix

1. MATRIX
Baiju P
Assistant Professor
Department of Economics
Kristu Jayanti College (Bengaluru)
11/10/2023

2. Introduction
• A matrix is a fundamental concept in mathematics and various
fields of science and engineering. It is a rectangular array of
numbers, symbols, or expressions organized in rows and
columns. Matrices are widely used to represent and manipulate
data, perform mathematical operations, and solve systems of
linear equations.
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3. Basics
• Rows and Columns: A matrix consists of rows and columns.
The number of rows is called the "row dimension," and the
number of columns is called the "column dimension." A matrix
with 'm' rows and 'n' columns is referred to as an "m x n" matrix.
• Elements: Each entry or element in a matrix is denoted by aij,
where 'i' represents the row number and 'j' represents the
column number. For example, a21 refers to the element in the
second row and first column.
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4. Fundamental rules, properties and types
of matrices
• Matrices obey various rules and properties that are important to
understand when working with them in linear algebra and
various mathematical applications.
• Here are some fundamental rules and properties of matrices:
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5. Matrix Addition and Subtraction:
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If A and B are two matrices of the same size (having the same number of rows and
columns), then they can be added or subtracted element-wise. The result is a new matrix
C, where each element c_ij is the sum (or difference) of the corresponding elements
from A and B.

6. Problems
• Problem 1:
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7. Scalar Multiplication:
You can multiply a matrix by a scalar (a single number) by multiplying every element of the
matrix by that scalar. If A is a matrix and k is a scalar, then kA represents scalar
multiplication.
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8. Matrix Multiplication:
If A is an m×n matrix and B is an n×p matrix, then their product AB is
defined, and the resulting matrix will be an m×p matrix. In matrix
multiplication, the number of columns in the first matrix must match the
number of rows in the second matrix
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9. Associative Property of Matrix Multiplication:
(AB)C = A(BC), where A, B, and C are matrices of appropriate
sizes.
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10. Distributive Property of Matrix Multiplication:
A(B + C) = AB + AC, and (A + B)C = AC + BC, where A, B, and C are
matrices of appropriate sizes.
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11. Distributive Property of Matrix Multiplication:
A(B + C) = AB + AC, and (A + B)C = AC + BC, where A, B, and C are
matrices of appropriate sizes.
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