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Vijay posted an Question
March 27, 2021 • 14:29 pm 30 points
  • IIT JAM
  • Mathematics (MA)

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

2 Answer(s) Answer Now
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    Deepak singh 1 Best Answer

    A set B is a basis of V if 1. its elements are linearly independent 2. every element of V is a linear combination of elements of B. Only this two conditions makes basis . Here , B={(a,b),(c,d)} , a,b,c,d€R can be made into basis if they satisfy above two conditions. And we can take many a,b,c,d . So , B is infinite . Thus , For any vector space , we can find infinite basis .

  • Alka gupta

    yes it can be....if it is LI set and spanned whole 2D space then this set form a basis

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    Satpal singh best-answer

    For any vector space there exist infinite bases. In this case if {(a,b),(c,d)} are L.I. or spanning set then it will become basis

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