f) V = R³; W = {(a, b, c) e IR³ |3a + 2b − c = 0} g) V = {ax² + bx + c a, b et c = R}; {ax² + bx + cb = 0, a et c = R} h) V = {ax² + bx + cla, b et ce R}; W = {ax² + bx + c/b = 1, a et c = R} =

f) V = R³; W = {(a, b, c) e IR³ |3a + 2b − c = 0} g) V = {ax² + bx + c a, b et c = R}; {ax² + bx + cb = 0, a et c = R} h) V = {ax² + bx + cla, b et ce R}; W = {ax² + bx + c/b = 1, a et c = R} =

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Let V be a vector space over R, equipped with the usual operations on algebraic vectors, polynomials and sequences, and W, a non-empty subset of V, equipped with the same operations. Determine if W is a vector subspace of V. If not, justify or find a counterexample.

la définition 56
W = {(a, b, c) e R³ 3a + 2b -c=0}
g) V = {ax² + bx + cla, b et c = R};
W = {ax² + bx + cb = 0, a et c = R}
h) V = {ax² + bx+cla, b et c = R};
W = {ax² + bx + c/b = 1, a et ce R}
i) V = {ax² + bx+cla, b et c e R};
W = {ax² + bx+c|a + b + c = 0}
j) V = {(a, a, a, ...) la € R};
W = {(a, a, a, ...) a = R}
21
=(f) V = R³;

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