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Linear algebra and sub spaces

  1. Dec 1, 2007 #1
    1. The problem statement, all variables and given/known data
    A) let T_k be all polynomials with degree 3 or under such that k is their coefficients sum.
    so we can say that exist at least 2 values of k for them T_k is the sub vector space of P_3(x)?
    B) this question is about direct sum: Let [tex]V_1,V_2,V_3[/tex] be subvector spaces of V if [tex]V_1 \cap V_2={0}[/tex] and [tex]V_1 \cap V_3={0}[/tex] than [tex]V_1 \cap (V_2+V_3)={0}[/tex]


    2. Relevant equations

    A) is this true??? am i right? look under for my answer

    3. The attempt at a solution

    A)i think this statment is false for example for k=2,4 we have T_k polynomials but T_k is not close under scalar multipication....is this right?

    B)i infact dont think the statement is true but i couldnt find an exaple to support it
     
  2. jcsd
  3. Dec 1, 2007 #2

    Dick

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    Science Advisor
    Homework Helper

    For A), k=2 or 4 don't work, you are right. But what if k=0? For B), yes, it's false. Take the space of linear polynomials P_1(x). Let V1 be all multiples of (1+x), V2 be all multiples of 1 and V3 be all multiples of x.
     
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