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Byju's Answer
Standard XII
Mathematics
Addition and Subtraction of a Matrix
If A = begin ...
Question

If A=⎡⎢⎣−123579−211⎤⎥⎦ and B=⎡⎢⎣−41−5120131⎤⎥⎦, then verify that
(i)(A+B)'=A'+B'

(ii)(A-B)'=A'-B'

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Solution

(i)Here, A+B=⎡⎢⎣−123579−211⎤⎥⎦+⎡⎢⎣−41−5120131⎤⎥⎦=⎡⎢⎣−53−2699−142⎤⎥⎦
⇒(A+B)′=⎡⎢⎣−56−1394−292⎤⎥⎦.....(i)
Also A′+B′=⎡⎢⎣−123579−211⎤⎥⎦′+⎡⎢⎣−41−5120131⎤⎥⎦′=⎡⎢⎣−15−2271391⎤⎥⎦+⎡⎢⎣−411123−501⎤⎥⎦=⎡⎢⎣−56−1394−292⎤⎥⎦........(ii)
From Eqs.(i)and (ii), it is verified that (A+B)'=A'+B'.

Here, A−B=⎡⎢⎣−123579−211⎤⎥⎦−⎡⎢⎣−41−5120131⎤⎥⎦

=⎡⎢⎣−1+42−13+55−17−29−0−2−11−31−1⎤⎥⎦=⎡⎢⎣318459−3−20⎤⎥⎦
⇒(A−B)′=⎡⎢⎣34−315−2890⎤⎥⎦.....(i)
Also, A′−B′=⎡⎢⎣−15−2271391⎤⎥⎦−⎡⎢⎣−411123−501⎤⎥⎦=⎡⎢⎣−1+45−1−2−12−17−21−33−(−5)9−01−1⎤⎥⎦⎡⎢⎣34−315−2890⎤⎥⎦.............(ii)
From Eqs.(i)and (ii), it is verified that (A-B)'=A'-B'.


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