Q. 764.7( 3 Votes )

Fill in the blank

Answer :

(i) (AB)’ = ________.


(AB)’ = B’A’


Let A be matrix of order m× n and B be of n× p.


A is of order n× m and B is of order p× n.


Hence B A is of order p× m.


So, AB is of order m× p.


And (AB) is of order p× m.


We can see (AB) and B A are of same order p× m.


Hence (AB) = B A


Hence proved.


(ii) (kA)’ = ________. (k is any scalar)


If a scalar “k” is multiplied to any matrix the new matrix becomes


K times of the old matrix.


Eg: A =


2A =


=


(2A) =


A =


Now 2A =


=


Hence (2A) =2A


Hence (kA)’ = k(A)’


(iii) [k (A – B)]’ = ________.


A =


A =


2A = 2


=


B=


B =


2B =


=


A-B =


Now Let k =2


2(A-B) =


=


[2(A-B)] =


2A – 2B =


=


A – B =


=


2(A – B) = 2


=


Hence we can see [k (A – B)]’= k(A)’- k(B)’= k(A’-B’)


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