Question: In this subsection we have shown that Gaussian reduction finds a basis for the row space. (a) Show that this basis is not unique-different reductions

In this subsection we have shown that Gaussian reduction finds a basis for the row space.
(a) Show that this basis is not unique-different reductions may yield different bases.
(b) Produce matrices with equal row spaces but unequal numbers of rows.
(c) Prove that two matrices have equal row spaces if and only if after Gauss-Jordan reduction they have the same nonzero rows.

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