1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Need help with vector space multiple choice

  1. Jan 21, 2010 #1
    Determine whether the given set S is a subspace of the vector space V.

    A. V=P5, and S is the subset of P5 consisting of those polynomials satisfying p(1)>p(0).
    B. V is the vector space of all real-valued functions defined on the interval [a,b], and S is the subset of V consisting of those functions satisfying f(a)=f(b).
    C. V=ℝn, and S is the set of solutions to the homogeneous linear system Ax=0 where A is a fixed m×n matrix.
    D. V=Mn(ℝ), and S is the subset of all n×n matrices with det(A)=0.
    E. V=P4, and S is the subset of P4 consisting of all polynomials of the form p(x)=ax3+bx.
    F. V=C2(I), and S is the subset of V consisting of those functions satisfying the differential equation yʺ=0.
    G. V=ℝ3, and S is the set of vectors (x1,x2,x3) in V satisfying x1-9x2+x3=8.
  2. jcsd
  3. Jan 21, 2010 #2
    S is a subspace of V if, (1) S is closed under addition (given two elements a and b in S, a+b is in S) and (2)S is closed under scalar multiplication (given x in S, and a scalar c, cx is in S).

    For each question you should see if the set satisfies these two criteria. If it doesn't then find a counterexample.

    For example problem D, does detA = 0 = detB mean that det(A+B) = 0?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Need help vector Date
Need help with this vector problem -- Thank you May 14, 2017
Vectors Need Help Feb 27, 2015
Need help with proof of Vector Space (Ten Axioms) Oct 31, 2014
Vector definition, need help Nov 18, 2012
Vector help needed Aug 10, 2012