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(Solved): (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], ...



(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

.

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