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Computational cost of solving $Ax_i = b_i$ for $i=1,…,m$

$A$ is an invertible matrix square $n$ matrix. The exercise is about 3 different ways you can solve this and I have to determine its efficiency. It's always the same matrix $A$ but a different right ...
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minmax of hamming weight in a basis for a vector space

Consider the vector space $V=\mathbb{Z}_2^n$ and take some linear subspace $U\subseteq V$ (we can assume we are given some basis for $U$). Now, for every basis $B$ of U, define $f(B)=\max_{b\in ...