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Anku posted an Question
May 02, 2021 • 18:54 pm 30 points
  • IIT JAM
  • Mathematics (MA)

Pls give an example for given statement

pls give an example for given statement. . .. . . .. . . ..

3 Answer(s) Answer Now
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    Gattu uday best-answer

    Yes obviously ... Every vector in vectorspace will generate another vector sooo if we take any number of vectors those will definitely generate the Vectorspace , but Basis is the minimal ( Smallest) subsetbof Vectorspace that generates entire Vectorspace the vectors more than the number of vectors of basis also generates entirely but less vectors can't generate entire Vectorspace , And more over BASIS IS THE MAXIMAL LINEARLY INDEPENDENT SET AND MINIMAL SPANNING SET, Soo spanning vectors obviously more than number of vectors of Basis or equal to the number of vectors in basis .☺️

  • comment-profile-img>
    Piyush pachauri best-answer

    Statement is true as cardinality of spanning set is always greater than equal to cardinality of LI vectors.

  • comment-profile-img>
    Deepak singh 1 Best Answer

    Refer attached example . no. of elements in spanning set is always greater than or equal to no. of elements in basis .

    cropped4404959764829799587.jpg
    eduncle-logo-app

    statement is correct .

    eduncle-logo-app

    sir can u pls once show how s is spanning V i.e. R³..i am not getting that

    eduncle-logo-app

    since S contains {(1,0,0),(0,1,0),(0,01)} which spans R^3 implies bigger set S also spans R^3.

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