Question
Let p0, p1, p2 and p3 be the following vectors of P2,R: p0(x) = x^2 + x, p1(x) = x^2 ?1, p2(x) = ?x +
Let p0, p1, p2 and p3 be the following vectors of P2,R: p0(x) = x^2 + x, p1(x) = x^2 ?1, p2(x) = ?x + 2 , p3(x) = x?2.
(i) Write each element of the set {1, x, x^2} as a linear combination of p0, p1, and p2. If you think this is not possible, just write "NP".
(ii) Consider the following sub-vector spaces of P2,R: F = Span(p0,p1), G = Span(p2,p3), F + G = Span(p0,p1,p2,p3).
What is the minimal number of vectors in a spanning set for F? And for G? And for (F + G)?
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Linear Algebra With Applications
Authors: W. Keith Nicholson
7th Edition
978-0070985100, 70985103
