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Matrix
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) 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 eth 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.   

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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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