mathmari Posted August 12, 2013 Share Posted August 12, 2013 Hi!!! I have the following exercise: describe the set of solutions of a linear system as a coset of an appropriate subspace. Could you give me an example? Link to comment Share on other sites More sharing options...
studiot Posted August 12, 2013 Share Posted August 12, 2013 Well a coset is a subspace plus an additional element(s) The kernel is a subspace but not necessarily the whole solution So whole solution is the kernel plus ..... Does this help? 1 Link to comment Share on other sites More sharing options...
mathmari Posted August 12, 2013 Author Share Posted August 12, 2013 Is the whole solution the kernel plus a particular solution? So if [tex] Ax_{0}=0 [/tex] and w is a soluion of [tex] Ax=b [/tex], then the whole solution is [tex] x_{0}+w [/tex] ?? Link to comment Share on other sites More sharing options...
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