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Question $2$

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Suppose a robot arena has $5$ mini robots, $3$ mid$-$size robots and $2$ big robots, and $57$ different skills that these robots possess. Let $M$ be an $(5+3+2)57$ matrix where $M_{ij}$ is $1$ if robot i possesses skill $j,$ and $0$ otherwise. Each mini robot has unique skills that other mini robots don't have, each mid$-$size robot has all the skills of all mini robots closer to them than other mid$-$size robots but no additional skills, and each big robots have all the skills of all mid$-$size robots closer to them than other big robots and NO ADDITIONAL SKILLS. Determine the rank of the matrix M$.$ Note: Below an example of a robot arena which is NOT related to parameters given in the question. For the example case shown, big robot $1$ will have the skills of mid robot $1$ and $2,$ and additional unique skill. Mid Robot $1$ will have the skills of mini robot $1$ and $2,$ but will not have additional unique skills.