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Linear AlgebraSuperchallengeVector Spaces & Bases

Vector Spaces & Bases · Superchallenge problem

Let VV be the set of all real sequences (an)n∈Z(a_n)_{n\in\mathbb{Z}} that satisfy, for every integer nn,

an+12=an,an+an+4+an+8=0,an+an+3+an+6+an+9=0.a_{n+12} = a_n,\qquad a_n + a_{n+4} + a_{n+8} = 0,\qquad a_n + a_{n+3} + a_{n+6} + a_{n+9} = 0.

VV is a vector space. What is dim⁡V\dim V?

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