Unformatted text preview: , 1 , 1], (that is at least two of a, b, c are distinct), then the left–to–right test shows that [ a, b, c ] and [1 , 1 , 1] are linearly independent and hence form a basis for R ( A ). Conse-quently rank A = 2 in this case. 11. Let S be a subspace of F n with dim S = m . Also suppose that X 1 ,...,X m are vectors in S such that S = h X 1 ,...,X m i . We have to prove that X 1 ,...,X m form a basis for S ; in other words, we must prove that X 1 ,...,X m are linearly independent. 36...
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- Fall '10
- Linear Algebra, basis, X1, xm