Let $S$be the set of all column matrices $[b_{1}b_{2}b_{3}]$such that $b_{1},b_{2},b_{3}∈R$and the system of equations (in real variable)$−x+2y+5z=b_{1}$$2x−4y+3z=b_{2}$$x−2y+2z=b_{3}$has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least one solution for each $[b_{1}b_{2}b_{3}]∈S$?(a) $x+2y+3z=b_{1},4y+5z=b_{2}$and $x+2y+6z=b_{3}$(b) $x+y+3z=b_{1},5x+2y+6z=b_{2}$and $−2x−y−3z=b_{3}$(c) $−x+2y−5z=b_{1},2x−4y+10z=b_{2}$and $x−2y+5z=b_{3}$(d) $x+2y+5z=b_{1},2x+3z=b_{2}$and $x+4y−5z=b_{3}$