Results 1 to 3 of 3

Math Help - Show Linearly Independent

  1. #1
    VkL
    VkL is offline
    Member
    Joined
    Oct 2008
    Posts
    96

    Show Linearly Independent

    Consider the set of vectors in the real vector space R3

    1 0 1
    3 1 p
    3 -p -1

    For what value(s) p is the set of vectors linearly independent?

    Ok, so. I think I'm on the right path.

    For A set of vectors to be Linearly independent, the determinent cannot = 0

    So i found the Det of that matrix to be p^2 - 3p - 4 and got that p cannot equal 4, or -1. Because that would make the det = zero.

    So is he answer all real numbers besides 4 and - 1?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    14,974
    Thanks
    1121
    Yes, that is completely correct.

    Note that a more fundamental definition of "independent vectors" is that a linear combination of them is 0 only if all coefficients are 0.

    Here such a linear combination would be a(1 0 1)+ b(3 1 p)+ c(3 - p -1)= (0 0 0) (or a(1 3 3)+ b(0 1 -p)+ c(1 p -1)= (0 0 0)- it was not clear whether your vectors were the rows or columns) which gives the equation a+ 3b+ 3c= 0, b- pc= 0, a+ pb- c= 0. Find the values of p for which those equations have only a= b= c= 0 as solution. Of course, that occurs when the determinant of the coefficient matrix is non-zero which leads right back to your solution.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    VkL
    VkL is offline
    Member
    Joined
    Oct 2008
    Posts
    96
    Yes, how you explained it is the general def. But thanks a lot for confirming.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. linearly dependent in Q, linearly independent in R
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: April 12th 2011, 01:44 PM
  2. Replies: 1
    Last Post: March 9th 2011, 08:42 PM
  3. Replies: 1
    Last Post: October 27th 2010, 05:41 AM
  4. linearly independent?
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: August 27th 2010, 09:53 AM
  5. Linearly Independent
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 25th 2007, 07:55 PM

Search Tags


/mathhelpforum @mathhelpforum