remarks for exam 2 in linear algebra span linear independence and basis the span of a set of vectors is the set of all linear combinations of the vectors a ...
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...Remarks for exam in linear algebra span independence and basis the of a set vectors is all combinations linearly independent if only solution to c v i k given you can determine they are by writing as columns matrix solving ax there any non zero solutions then dependent x abasis subspace s rn that spans many bases but every must have exactly dim spanning contain at least most with rank nullity thespanoftherowsofmatrixaistherowspaceofa thespanofthecolumnsofaisthecolumn space row column spaces always same dimension called let r maximal number so n m rows rref pivots both dimensions four fundamental null pivot form be an its other words together gives u has full rm system b unique innitely inconsistent e not following statements equivalent invertible...