(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Define a non-zero linear functional y on C^2 such that if x_{1}=(1,1,1) and x_{2}=(1,1,-1), then [x_{1},y]=[x_{2},y]=0.

2. Relevant equations

N/A

3. The attempt at a solution

Le X = {x1,x2,...,xn} be a basis in C^{3}whose first m elements are in M (and form a basis in M). Let X' be the dual basis in C^{3}'. Let N be the subspace of V' spanned by y_{m+1}, ..., y_{n}.

Let's assume that y is any element in N.

1) y is in V'

2) y is a linear combination of the basis vectors y_{1}, ..., y_{n}

=> y = [tex]\Sigma[/tex]_{j=1}^{n}n_{j}y_{j}

Since by assumption y is in N we have for every i=1,...,m

[x_{i},y] =0

P.S: I am new to the abstract linear algebra world.

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# Homework Help: Abstract Linear Algebra: Dual Basis

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