Assume I have a known matrix $X$ of size, for example, $(16$ x $16)$, and a vector $z$ of size $(1$ x $16)$ where only some equispaced values are known, for example $1:4:16$ or values in locations $(1,5,9,13)$ in $z$ are known and others values are unknown. If we have $y = z*X$; I need to set the known values in $z$ which are located in $(1,5,9,13)$ to such numbers such that to have ones in the same locations in $y$. Is there any algorithm or method I can use to do that ? Is that possible?


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