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Finding the dimension of the vector space spanned by 3 vectors

  • 29-04-2010 10:14PM
    #1
    Registered Users, Registered Users 2 Posts: 2,906 ✭✭✭


    Anyone know of any good tutorials or guides on finding the dimension of a vector space spanned by 3 vectors ?? Haven't a clue how to approach it :(


Comments

  • Registered Users, Registered Users 2 Posts: 2,481 ✭✭✭Fremen


    Mind posting up the specific problem?


  • Registered Users, Registered Users 2 Posts: 2,906 ✭✭✭cian1500ww


    Fremen wrote: »
    Mind posting up the specific problem?
    Sure:
    Consider the set of vectors V = fv1 = (1; 2; 1; 2); v2 = (1; 1; 1; 1); v3 =
    (0; 0; 0; 1); v4 = (0; 1; 2; 0)g.
    (i) What is the dimension of the vector space spanned by the vectors in V ?

    It's for a maths assignment so I'm not looking for the answer (unfortunately :rolleyes:) Just how to solve it basically. Thanks !!


  • Registered Users, Registered Users 2 Posts: 271 ✭✭Clinker


    Gaussian elimination will produce a linearly independent set with the same span.


  • Registered Users, Registered Users 2 Posts: 2,481 ✭✭✭Fremen


    Yup, use Gaussian elimination to make as many zero rows as possible. Once you're done, the number of non-zero rows is the dimension of the subspace.


  • Registered Users, Registered Users 2 Posts: 2,906 ✭✭✭cian1500ww


    Thanks for the help guys, much appreciated :)


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