Row Reduction & Rank · Hard problem

A structural model has four strain readings fitting three unknown deflections $x,y,z$: $x+y+z=9$, $x-y+z=3$, $2x+y-z=3$, and $3x-y+2z=b$. The first three readings already determine $x,y,z$ uniquely. For what value of $b$ is the fourth reading consistent with (not contradicting) the first three?