Results 1 to 4 of 4

Math Help - polynomial subspaces

  1. #1
    Banned
    Joined
    Feb 2009
    Posts
    97

    polynomial subspaces

    Which of the following subsets of P_{2} are subspaces? The set of all polynomials of the form:
    a. a_{2}t^{2}+a_{1}t+a_{0}, where a_{1}=0 and a_{0}=0
    b. a_{2}t^{2}+a_{1}t+a_{0}, where a_{1}=2a_{0}
    c. a_{2}t^{2}+a_{1}t+a_{0}, where a_{2}+a_{1}+a_{0}=2
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by antman View Post
    Which of the following subsets of P_{2} are subspaces? The set of all polynomials of the form:
    a. a_{2}t^{2}+a_{1}t+a_{0}, where a_{1}=0 and a_{0}=0
    b. a_{2}t^{2}+a_{1}t+a_{0}, where a_{1}=2a_{0}
    c. a_{2}t^{2}+a_{1}t+a_{0}, where a_{2}+a_{1}+a_{0}=2
    To be a suspace we require for the set to be closed under addition and scalar multiplication.
    Check if this is true for each of these cases.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Banned
    Joined
    Feb 2009
    Posts
    97
    So then a and b would be subspaces? C would not be because if it is multiplied by zero, the conditions a2+a1+a0=2 would not be satisfied. When b is multiplied by 0 to get 0+0+0, a_1=2_a0 because 0=2(0) and 0=0?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by antman View Post
    So then a and b would be subspaces? C would not be because if it is multiplied by zero, the conditions a2+a1+a0=2 would not be satisfied. When b is multiplied by 0 to get 0+0+0, a_1=2_a0 because 0=2(0) and 0=0?
    Yes, , (a) and (b) are subspaces but (c) is not.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Subspaces of polynomial vector space
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: May 13th 2010, 08:40 AM
  2. Replies: 0
    Last Post: October 13th 2009, 03:48 PM
  3. need help for subspaces
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 16th 2008, 04:54 PM
  4. Subspaces
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: October 31st 2007, 06:17 PM
  5. Subspaces
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 4th 2007, 03:35 AM

Search Tags


/mathhelpforum @mathhelpforum