Exercise 3.F.9

Answers

Proof. Let $c_{1}, \dots, c_{n} \in 𝔽$ such that

ψ = c_{1} φ_{1} + \dots + c_{n} φ_{n}

Therefore

ψ (v_{j}) = c_{1} φ_{1} (v_{j}) + \dots + c_{n} φ_{n} (v_{j}) = c_{j}

Substituting this in the previous equation for each $j$ we get

ψ = ψ (v_{1}) φ_{1} + \dots + ψ (v_{n}) φ_{n}

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celiopassos

2017-10-06 00:00