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Let A be an mxn matrix. Show that the set of all solutions to the homogeneous...

Let A be an mxn matrix. Show that the set of all solutions to the homogeneous equation Ax=0 is a subspace of R^n and the set of all vectors b such that Ax=b is consistent is a subspace of R^m. Is the set of solutions to a non-homogeneous equation Ax=b a subspace of R^n? Explain why or why not.

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