1.Determine whether the set C2 with the operations: (a, b) + (c, d) = (a, b) and k(a, b) = (ka, kb) is a vector space over C. If it is, verify each vector space axiom; if it is not, state all vector space axioms that fail. 2.Let W = M2×2(C) be a symmetric matrix. Determine whether W is a subspace of V = M2×2(C) over C.

1.Determine whether the set C2 with the operations: (a, b) + (c, d) = (a, b) and k(a, b) = (ka, kb) is a vector space over C. If it is, verify each vector space axiom; if it is not, state all vector space axioms that fail. 2.Let W = M2×2(C) be a symmetric matrix. Determine whether W is a subspace of V = M2×2(C) over C.

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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