linear algebra – What are the conditions on the components of b such that b \$ in \$ col (A)?

I do not know now how to write the matrix below with parentheses, so it will be appreciated if someone can add them.

Let b = $$(b_1, b_2, b_3, b_4) ^ T$$ $$in$$ $$R ^ 4$$

and
(R |there) =$$begin {array} {cccc | c} -1 & -3 & 1 & 1 & b_1 \ 0 & -1 & 1 & 2 & 3b_1 + b_2 \ 0 & 0 & 0 & 0 & -8b_1-2b_2 + b_3 \ 0 & 0 & 0 & 0 & -b_1 + 2b_2 + b_4 \ end {array}$$

i) What are the conditions on the components of b such as b $$in$$ Cola)?

I tried to leave $$x_3$$ and $$x_4$$ to be a free variable, but I do not think it requires the duration of something.

ii) Find a matrix $$C$$ such that col (A) = ker (C).