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Linear Algebra help :(

  • 07-10-2013 05:15PM
    #1
    Registered Users, Registered Users 2 Posts: 3


    Hi,

    I have a homework assignment for Linear Algebra and I have done most of it right so far but I really cannot understand these two questions :(

    Q1. Which of the following subsets of P2 are subspaces of P2?

    A. { p(t) | p'(t) + 7 p(t) + 9 =0}
    B. { p(t) | p(-t)= p(t) for all t}
    C. { p(t) | p'(t) is constant}
    D. { p(t) | int from 0 to 3 p(t)dt = 0}
    E. { p(t) |p'(2)= p(8)}
    F. { p(t) | p(6)= 4}

    Q2. Which of the following sets are subspaces of R^3?

    A. { (x,y,z) | x + y + z = 6}
    B. { (x, x+2, x - 8) | x arbitrary number}
    C. { (-6 x - 7 y, 4 x - 9 y, 3 x + 9 y ) | x,y arbitrary numbers}
    D. { (x, 0, 0) | x arbitrary number}
    E. { (x,y,z) | x < y < z}
    F. { (x,y,z) | x + y + z = 0}

    I'd really appreciate any help anybody could give me!! :)

    Thanks!


Comments

  • Registered Users, Registered Users 2 Posts: 427 ✭✭sigmundv


    I assume they mean "linear subspace". Then you need to apply the following theorem in each case; if it holds, the subset is a subspace.

    Theorem:
    Let V be a vector space over the field K, and let W be a subset of V. Then W is a subspace if and only if W satisfies the following three conditions:
    1) The zero vector, 0, is in W.
    2) If u and v are elements of W, then the sum u + v is an element of W;
    3) If u is an element of W and c is a scalar from K, then the product cu is an element of W.

    http://en.wikipedia.org/wiki/Linear_subspace


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