We can show that every basis for R3 contains the same number of vectors. (a) Show that
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(a) Show that no linearly independent subset of R3 contains more than three vectors.
(b) Show that no spanning subset of R3 contains fewer than three vectors. Recall how to calculate the span of a set and show that this method cannot yield all of R3 when we apply it to fewer than three vectors.
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a Any four vectors from R 3 are linearly related because the vector equation gives rise to a linear ...View the full answer
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