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Matrix Multiplication

Let

and,

be two

Then the product of these two matrices is defined as an

where

= Sum of the products of the elements of

The product matrix

In the product

Thus we notice that the product

Two matrices

**A = [a**,_{ij}]**I = 1, 2, …, m; j = 1, 2, …., n**and,

**B = [b**_{jk}], j = 1, 2, …., n; k = 1, 2, …., pbe two

**m × n**and**n × p**matrices respectively such that the number of rows of**B**is the same as the number of columns of**A**.Then the product of these two matrices is defined as an

**m × p**matrix**C = AB = [c**_{ik}], I = 1, …., m; k = 1, …, pwhere

**c**_{ik}= a_{i1}b_{1k}+ a_{i2}b_{2k}+ ….. + a_{in}b_{nk}= b_{ik}= Sum of the products of the elements of

**i**^{th}row and**j**^{th}columns of**A**with the corresponding elements of**j**row and^{th}**k**columns of^{th}**B**.**Note: c**_{ik}is obtained by multiplying the elements in the**i**^{th}row of**A**with the corresponding elements in the**k**^{th}column of**B**and then adding them.The product matrix

**AB**will have**m**rows and**p**columns, i.e. if**A**is an**m × n**matrix and**B**is**n × p**matrix, then**AB**is an**m × p**matrix.In the product

**AB**,**A**is known pre-factor and**B**as post-factor.Thus we notice that the product

**AB**is defined if and only if the number of columns of the pre-factor is equal to the number of rows of the post-factor.Two matrices

**A**and**B**are said to be comfortable for multiplication if the number of columns of**A**is equal to the number of rows of**B**.**Note:**It is important to note that there can be matrices which are not comfortable for multiplication and in that case we say that the multiplication of the matrices is not defined. We consider a few examples to illustrate the above data.**Services: -**Matrix Multiplication Homework | Matrix Multiplication Homework Help | Matrix Multiplication Homework Help Services | Live Matrix Multiplication Homework Help | Matrix Multiplication Homework Tutors | Online Matrix Multiplication Homework Help | Matrix Multiplication Tutors | Online Matrix Multiplication Tutors | Matrix Multiplication Homework Services | Matrix MultiplicationSubmit Your Query ???

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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
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Algebra Fundamental Theorem
Gaussian Integer
Geometric Series
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Infinite Series Convergent
Integers
Inverse Of Square Matrix
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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
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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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