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ADDITION AND SUBTRACTION OF MATRICES

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Addition of Matrices

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The sum of two matrices is obtained by adding the corresponding elements of both the matrices.  While adding two matrices, their order must be the same.
In general, if A = [aij] and B = [bij] are two matrices of same order then the sum of A and B is given by matrix C = [cij] where cij = aij + bij for all possible values of i and j.

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Properties of Matrix addition

i) Commutative Law: If A and B are any two matrices of same order then    A + B = B + A
ii) Associative Law: If A, B and C are any three matrices of same order then A + (B + C) = (A + B) + C
iii) Existence of additive identity: Let A be a matrix of order m x n and 0 be an m x n zero matrix, then A + 0 = 0 + A.
iv) Existence of additive inverse: Let A be any matrix, then we can find another matrix –A such that A + (-A) = 0.  So additive inverse of A is –A.

Difference of two matrices


If A and B are two matrices of same order, then the difference A - B is obtained by subtracting the corresponding elements of A and B.


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Find 2 A + B

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Find A – B
3. Find the values of x and y given the following equation:

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Reference Links:

http://en.wikipedia.org/wiki/Matrix_(mathematics)

http://en.wikipedia.org/wiki/Commutativity

http://en.wikipedia.org/wiki/Associativity

http://en.wikipedia.org/wiki/Additive_identity

http://en.wikipedia.org/wiki/Additive_inverse

    

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