If the relation $a_{ij}u^iu^j=0$ holds for all vectors $u^i$ such that $u^i\lambda_i=0$ where $\lambda_i$ is a given covariant vector, show that
$$a_{ij}+a_{ji}=\lambda_iv_j+\lambda_j v_i$$ where $v_j$ is some covariant vector.
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