(28pts) Let
A=([1,5,-2,-1,1],[2,1,-1,-2,-1],[0,2,3,0,8],[-1,0,3,1,6],[-1,3,-2,1,-1]),B=([0],[1],[1],[(1)/(3)],[-(4)/(3)]),vec(x)=([x_(1)],[x_(2)],[x_(3)],[x_(4)],[x_(5)])
, and
vec(O)=([0],[0],[0],[0],[0])
. a) Determine the rank of
A
. b) Find the solution space of the system
A*x=O
. c) Determine the dimension of the solution space. d) Find the general solution of the non-homogeneous system
Ax=B
.