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MHT-CET : Mathematics Entrance Exam

MHT - CET : Mathematics - Matrices Formulae Page 1

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 1. Equality of Two Matrices:

 

If A = [aij] and B = [bij]are the two matrices of same order then they are said to be equal if their corresponding elements are same.
i.e., A = B if aij =bij for all i and j.

 

 2. Addition and Subtraction of Two Matrices:

 

If A = [aij]m n and B = [bij]m n then
A + B = [aij + bij]m
n and A B= [aij bij]m n for all i and j.

 

 3. If A, B, C are three matrices of same order, then

 

(i) 

A + B = B + A, Commutative law.

(ii) 

A + (B + C) = (A + B) + C, Associative law

(iii) 

A + 0 = 0 + A = A, where 0 is a null matrix

 

 4. Multiplication of two Matrices:

 

If A = [aij]m n and B = [bjk]n p are two matrices then the product C = AB = [Cik]m n where Cik can be obtained by multiplying the ith row of A and kth column of B.

 

 5. Properties of Matrix Multiplication :

 

If A, B, C are three matrices, then

 

AB BA (in general)

 

A(BC) = (AB)C, associative law.

 

A(B + C) = AB + AC
(A + B)C = AC + BC

distributive law.

 

A.0 = 0.A = 0, where 0 is a null matrix.

 

A.I = I.A = A, where I is an identity matrix.

 

 6. Properties of Transpose :

 

If A and B are two matrices and k is a scalar, then

 

 7. Some useful results:

 

 

 8. Some useful properties:

 

 

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