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Unformatted text preview: 0 0 0 + f 0 0 0 0 0 0 0 0 1 so the set T = { 1 0 0 0 0 0 0 0 0 , 0 1 0 0 0 0 0 0 0 , 0 0 1 0 0 0 0 0 0 , 0 0 0 0 1 0 0 0 0 , 0 0 0 0 0 1 0 0 0 , 0 0 0 0 0 0 0 0 1 } spans S . T is certainly linearly independent since if we had a 1 0 0 0 0 0 0 0 0 + b 0 1 0 0 0 0 0 0 0 + 1 c 0 0 1 0 0 0 0 0 0 + d 0 0 0 0 1 0 0 0 0 + e 0 0 0 0 0 1 0 0 0 + f 0 0 0 0 0 0 0 0 1 = 0 0 0 0 0 0 0 0 0 then a b c d e 0 0 f = 0 0 0 0 0 0 0 0 0 so that a = b = c = d = e = f = 0. Hence the set T forms a basis for S . Since T has 6 elements, dim S = 6. 2...
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 Spring '10
 Peters
 Linear Algebra, Vector Space, Howard Staunton, upper triangular matrices

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