establish independence as "solutions are unique" #621
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Oh and we should probably an activity about the special homogeneous case (since we know a solution exists, it must be unique). |
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Activity 2.4.5 is the key reworked activity to consider here. |
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Closes #618. WIP.
Basic idea: have the same canonical equation
linear combo = arbitrary vectorused for both spanning and independence. We say a set is spanning provided this equation always has a solution, that is, it has 1 or more solutions. We say a set is independent provided any solution must be unique, that is, it has at most 1 solution. Put together, a set is a basis provided this equation always has a unique solution.If this is acceptable, work is required to align future activities to match.