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The student is already familiar with the system of simultaneous linear equations. For example, the equation

is a system of two linear equations in two unknown (variables)

The left-hand side of

In this arrangement, the entry

Consider, the system of equations

These are two linear equations in three variables

Each array of the kind given by

The numbers which constitute the matrix are called its entries or elements. In the above examples, we have considered the elements or entries to be real numbers. They could be complex numbers.

For each element or entry of a matrix, its value as well as its position both is important. For example, in the matrices

The elements in both the cases are either

is a system of two linear equations in two unknown (variables)

**x**and**y**.The left-hand side of

**(I)**is completely known if we know the coefficients of various equations. We arrange these coefficients in a block as given below.In this arrangement, the entry

**[3, 5]**in the top horizontal line is called the first row and it indicates the coefficients of**x, y**of the first equation**3x + 5y = 2**, of the system**(I)**.**The entries****[6, 1]**in the second horizontal line is called the second row and it indicates the coefficients of**x, y**in the equation**6x + y = 3**of the system**(I)**. the entries the first vertical line of**(II)**, is called the first column of the block**(II)**; and are the coefficients of**x**in the system**(I)**, whereas the entries**the second vertical line of****(II)**is called the second column of the block**II**, and are coefficients of**y**in**e**^{th}system of equation**(I)**. Thus the block gives all information about the left-hand side of**(I)**.**Similarly, the column gives all the information on the right hand side of****(I)**.Consider, the system of equations

These are two linear equations in three variables

**x**,**y**and**z**. This system of equation is fully specified by the block of array.Each array of the kind given by

**(II)**or**(IV)**is called a matrix.The numbers which constitute the matrix are called its entries or elements. In the above examples, we have considered the elements or entries to be real numbers. They could be complex numbers.

For each element or entry of a matrix, its value as well as its position both is important. For example, in the matrices

The elements in both the cases are either

**0**or**2**;**but the matrices are different as the elements in the identical positions are not the same. Thus a matrix is not just a collection of elements, but it is a collection in which each array has a definite position, i.e. it is an ordered array of elements.****Services: -**Matrix Homework | Matrix Homework Help | Matrix Homework Help Services | Live Matrix Homework Help | Matrix Homework Tutors | Online Matrix Homework Help | Matrix Tutors | Online Matrix Tutors | Matrix Homework Services | MatrixSubmit Your Query ???

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Topics

Real Number Absolute Value
Addition Of Matrices
Square Matrix Adjoint
Algebraic Structures
Alternating Series
Linear Equations Determinants
Archimedean Real Numbers
Binary Operation
Binary Relation In A Set
Bounded, Unbounded Sets
Cauchy Root Test
Caylay Hamiltion Theorem
Circular Permutation
Common Roots
Complex Numbers
Complex Number Conjugate
Conjugate Of A Matrix
Constant Sequences
Convergence Of A Sequence
Cosets
Cubic, Biquadratic Equations
De Moivre Theorem
Real Number Denseness
Order 3 Determinants
Differences Of Matrices
Direct Sum Of Vector Subspaces
Eigen Vector
Elementary Matrices
Matrix Elem. Transformations
Equal Matrices
Equal Roots
Two Permutations Equity
Equivalent Matrices
Trigonometry Function Expansion
Field
Function
Algebra Fundamental Theorem
Gaussian Integer
Geometric Series
Group
Ideals
Quantity Increasing Roots
Infinite Series Convergent
Integers
Inverse Of Square Matrix
Inverses Of Elementary Matrices
Iota, Imaginary Numbers
Left-Right Identity
Sequence Limit Points
Linear Combination Vectors Span
Linear Dependence, Independence
Linear Homogeneous Equations
Two Subspaces Linear Sum
Matric Polynomial
Matrix
Linear Equation Matrix Inverse
Matrix Multiplication
Matrix Scalar Multiplication
Method Of Difference
Minors And Co-factors
Multiplication Modulo P
Normal Sub-Group
Normalizer Or Centalizer
Orbit Of Permutation
Peano Axioms
Permutation Function
Pigeon Hole Principle
Matrices Integral Powers
Mathematical Induction Principal
Two Determinants Product
Two Permutations Product
Properties Of Modulus
Rank Of A Matrix
Rational Numbers
Rational, Integral Polynomial
Reciprocal Roots
Relation Of Sets
Rings Of A Set
Row By Column Matrix
Sequence
Series
Series Of Positive Terms
Series Partial Sum Sequence
Subrings
Sum Of A Series
Cosine Series Sum
Sum Of Sine Series
Symmetric/Skew Symm. Matrices
Roots Symmetric Functions
Symmetric Set Degree N
Synthetic Division
Transformation In General
Transformations Of Equations
Transpose Of A Matrix
Matrix Transposed Conjugate
Transposition
Complex Numbers Representation
Vector Space
Vector Sub-spaces
Whole Numbers
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