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Let S be the set of all column matrice...

Let `S` be the set of all column matrices `[b_1b_2b_3]` such that `b_1,b_2, b_3 in 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_1b_2b_3] in 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+10 z=b_2` and `x-2y+5z=b_3` (d) `x+2y+5z=b_1, 2x+3z=b_2` and `x+4y-5z=b_3`

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