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Linear Independence

  • 23-12-2010 5:32pm
    #1
    acb
    Registered Users, Registered Users 2 Posts: 120 ✭✭


    Have just a general query about LD or LI stuff!

    If we work out some question and we find it it LI... are we then saying it has only one solution and that is is the zero vector

    If we find its not LI ie is linear dependent then they are many solutions are they are non zero solutions?

    Are we saying all this then to talk about spanning sets and basis???
    Like is a LI set a minimal spanning set (basis) then?



    (Have only started studying and trying to link this stuff togeather -have an algebra exam in January, so apologies if it seems like a stupid question!)


Comments

  • #2
    Eliot Rosewater
    Registered Users, Registered Users 2 Posts: 3,745 ✭✭✭Eliot Rosewater


    acb wrote: »
    If we work out some question and we find it it LI... are we then saying it has only one solution and that is is the zero vector

    Yup.

    If a set of vectors is linearly independent then no one element can be represented as a linear combination of the others. This is equivalent to what you're saying.
    acb wrote: »
    If we find its not LI ie is linear dependent then they are many solutions are they are non zero solutions?

    Yup.
    acb wrote: »
    Are we saying all this then to talk about spanning sets and basis???
    Like is a LI set a minimal spanning set (basis) then?

    Yes. A basis is a set under two conditions:
    1. It is a spanning set.
    2. It is linearly independent.


  • #3
    acb
    Registered Users, Registered Users 2 Posts: 120 ✭✭acb


    Thank you!!!!


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