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suppose a got a matrix
A=
1 -2 2 3 -1
-3 6 -1 1 -7
2 -4 5 8 -4
and i have found the basis of Nul(A)
is span ( [2,1,0,0,0] ,[1,0,-2,1,0] ,[ -3,0,2,0,1] )
( v[1] , v[2] , v[3] )
from my tutorial sheet
i am suppose to find v[4] such that A.v[4] =[1,-3,2]
v[5] suh that A.v[5] =[0,5,1 ]
my question is how to find v4 and v5 ? are they unique? (i dont think they are )
and how to prove that v[1],v[2],v[3],v[4],v[5] are the basis of R^5
thanks
Chen
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