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Vijay posted an Question

May 01, 2021 • 12:07 pm

30 points

IIT JAM
Mathematics (MA)

Please send the solution to the problem given in the attachment.

please send the solution to the problem given in the attachment.

3 Answer(s)

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Gattu uday

Noo u,v are not supposed to be different in this case ,you have to take the elements ,if there are many elements you can take differently but here 0 is the only element soo you can take it for many times
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Gattu uday

{0} is subspace for all Vectorspaces ,it is called Improper subspace nd Trivial subspace , for checking take 0+0 like this every element for checking is 0
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Deepak singh 1 Best Answer

Refer attached
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in 2 , since W contains only one element 0 , so u=v=0 .
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ok, u and v don't have to be different, right?
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if a set contains a single element , then how we can take different element . So if we take different element , it will be equal and equal to that single element .
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Alka gupta

{0} and V both are called trivial subspace of vector space V . if W={0} then it is full fill all three conditions which is here mentioned 1. 0€V hence 0€W 2. u=0 , v=0 hence 0+0 =0 €W 3. c€W , 0€W hence c.0 =0 €W
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doubt--->aren't u and v supposed to be different elements in the 2nd statement?
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no....not necessary both must be different
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we can consider same elements also....
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