Results 1 to 3 of 3

Math Help - Some Simple True/False

  1. #1
    Junior Member
    Joined
    Feb 2010
    Posts
    56

    Some Simple True/False

    Hello everyone. I have a practice test and there are some T/F questions on it. I don't know the answers for sure but I have guesses. Can you please tell me what the answers are and possibly explain?

    True/False?:
    1. P2 is a Subspace of P3 (I think it's true)
    2. D[0,1], the set of all differential functions over [0,1] is a subspace of C[0,1] (I think it's true)
    3. {ax^2 + bx + c : b = 0} is a subspace of P2 (I think it's true....or maybe not)
    4. There is a basis for P3 which contains the function f defined by f(x) = x^2 - x + 1 (True..(x^2, -x, 1)?)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by chickeneaterguy View Post
    Hello everyone. I have a practice test and there are some T/F questions on it. I don't know the answers for sure but I have guesses. Can you please tell me what the answers are and possibly explain?

    True/False?:
    1. P2 is a Subspace of P3 (I think it's true)
    2. D[0,1], the set of all differential functions over [0,1] is a subspace of C[0,1] (I think it's true)
    3. {ax^2 + bx + c : b = 0} is a subspace of P2 (I think it's true....or maybe not)
    4. There is a basis for P3 which contains the function f defined by f(x) = x^2 - x + 1 (True..(x^2, -x, 1)?)

    All of them are true, and here are some hints: (1) is any polynomial of degree at most 2 a pol. of degree at most 3? ; (b) Is every differentiable function a continuous one? ; (c) Is the set of all pol's of degree at most 2 with zero linear coefficient a vector space? ; (d) Is is true that any non-zero vector in any non-zero vector space is part of some basis?

    Tonio
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Feb 2010
    Posts
    56
    Quote Originally Posted by tonio View Post
    All of them are true, and here are some hints: (1) is any polynomial of degree at most 2 a pol. of degree at most 3? ; (b) Is every differentiable function a continuous one? ; (c) Is the set of all pol's of degree at most 2 with zero linear coefficient a vector space? ; (d) Is is true that any non-zero vector in any non-zero vector space is part of some basis?

    Tonio
    Thanks.

    (1) Makes sense... 0x^3 + x^2 + x + 1 = x^2 + x + 1
    (2) Yeah. Makes sense. I was thinking C was something else for some reason.
    (3) Yep. No explanation.
    (4) I just learned basis...so I wasn't really sure.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Very simple true or false
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 17th 2011, 12:50 PM
  2. Replies: 7
    Last Post: October 5th 2011, 01:45 PM
  3. Replies: 1
    Last Post: October 4th 2011, 03:19 AM
  4. how come false AND false is true?
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: September 24th 2010, 08:41 AM
  5. True or False. Prove if true show counter example if false.
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: March 2nd 2010, 11:54 AM

Search Tags


/mathhelpforum @mathhelpforum