For each of the following matrices A:
(a) Determine the rank and the dimensions of the four fundamental subspaces.
(b) Find bases for both the kernel and cokemel.
(c) Find explicit conditions on vectors b which guarantee that the system Ax = b has a solution.
(d) Write down a specific nonzero vector b that satisfies your conditions, and then find all possible solutions x.
(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

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