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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
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Bounded, Unbounded Sets
Cauchy Root Test
Caylay Hamiltion Theorem
Circular Permutation
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Complex Numbers
Complex Number Conjugate
Conjugate Of A Matrix
Constant Sequences
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De Moivre Theorem
Real Number Denseness
Order 3 Determinants
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Direct Sum Of Vector Subspaces
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Matrix Multiplication
Matrix Scalar Multiplication
Method Of Difference
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Multiplication Modulo P
Normal Sub-Group
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Orbit Of Permutation
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Permutation Function
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Matrices Integral Powers
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Two Determinants Product
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Properties Of Modulus
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