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December 22nd, 2018, 01:35 AM   #1
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Question 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 progressing… Can anybody help out?

Let A be a matrix over R of order 4x4, with rank 2.
Suppose that the vectors
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.
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January 11th, 2019, 07:36 AM   #2
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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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