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 December 22nd, 2018, 02:35 AM #1 Newbie   Joined: Dec 2018 From: Tel Aviv Posts: 4 Thanks: 0 Matrix in relation to solution subspace Hi guys, I am having serious trouble analysing the following question: I have been thinking about it for an hour, but I am not progressingâ€¦ Can anybody help out? Let A be a matrix over R of order 4x4, with rank 2. Suppose that the vectors u=(2,1,2,0) v=(1,-1,2,4) w=(1,0,2,-1) are solutions to the linear system Ax=b. a. find the dimension of the solution space of the system Ax=0 and find its basis. b. find the general solution to the system Ax=b.
 January 11th, 2019, 08:36 AM #2 Senior Member   Joined: Mar 2015 From: New Jersey Posts: 1,641 Thanks: 119 If A has rank 2 it will have 2 linear independent cols, a basis, which span the solution space, of dim 2. Ax=b has a solution for any b in the solution space.

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