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Suppose, there is a system of linear equations $Ax = b$, where $A \in R^{m \times n}, m>n$ and $b_i \in \{l_1,....,l_k\}$, i.e. each $b_i$ is a label instead of being a real number.

To solve this, we can regroup the left hand sides which have the same label and we have such sets of such equations for each label. I think this would give us an under-determined system of equations. How would one solve it?

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