# Answer to Question #35203 in Linear Algebra for matthew lind

Question #35203

Please prove the following lemma by showing that if M > N, then there is a non-zero vector x such that Cx = Ax = 0:

lemma: Let W = {w^1,...,w^N} be a spanning set for a subspace S in R^I, and let {v^1,...,v^M} be a linearly independent subset of S. then M <= N.

lemma: Let W = {w^1,...,w^N} be a spanning set for a subspace S in R^I, and let {v^1,...,v^M} be a linearly independent subset of S. then M <= N.

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