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).