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Math Help - subspace of F -exams!

  1. #1
    n22
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    subspace of F -exams!

    Hi I need help with this .
    The lecturers at uni always say that I must test if zero is in the vector space .if its not ,then apparently its not a vector space.
    But sometimes its not always possible.-when is it not possible?
    THanks.
    This is the actual question.
    Let X={f which is a element of F such that f(x)=A+Be^x, A,B is an element of R}
    Justify and determine if X is subspace of F.
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    Re: subspace of F -exams!

    Hey n22.

    Hint: What are the sub-space axioms? (There are three of them).
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    n22
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    Re: subspace of F -exams!

    Hi Chiro,

    1.that S is not empty (check by chucking in zero)
    2.S closed under addition
    3.S is closed under scalar multiplication

    f(o)=A+B...its not equal to zero so....does that matter?when does it mater and when does it not?
    Let g(x)=C+De^x ....
    by addition,A+C +(B+D)e^x
    kf(x)=KA+kBe^x..
    i feel like the set up is kindda wrong..
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    Re: subspace of F -exams!

    You need to check that the zero vector is in the sub space. Can you do that?
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    Re: subspace of F -exams!

    Quote Originally Posted by n22 View Post
    Hi Chiro,

    1.that S is not empty (check by chucking in zero)
    2.S closed under addition
    3.S is closed under scalar multiplication

    f(o)=A+B...its not equal to zero so....does that matter?when does it mater and when does it not?
    Do you mean f(0)? That is not relevant. You want the zero vector, that is the function such that f(x)= 0 for all x, in the set.
    A and B here can be any real numbers. What do you get if you take A= B= 0?

    Let g(x)=C+De^x ....
    by addition,A+C +(B+D)e^x
    Which is of the form "A+Be^x" with A+ C instead of A and B+ D instead of B.
    You probably don't need to specifically state that A+ C and B+D are real numbers!

    kf(x)=KA+kBe^x..
    Which is of the form "A+ Be^x" with kA instead of A and kB instead of B.

    i feel like the set up is kindda wrong..
    Thanks from n22
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