Mathematics

13 June, 20:00

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 cokernel.

(c) Find explicit conditions on vectors b that 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.

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