Kunze Linear Algebra · Problem 2.1.5

Vector Spaces

Mathematics — Methods · vector-space-axioms

Problem

On RnR^n, define two operations α⊕β=α−β\alpha \oplus \beta = \alpha - \beta c⋅α=−cα.c \cdot \alpha = -c\alpha. The operations on the right are the usual ones. Which of the axioms for a vector space are satisfied by (Rn,⊕,⋅)(R^n, \oplus, \cdot)?

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