Unformatted text preview: / ∈ span( S 1 ), and consider the set S 2 = S 1 S { v k +2 } . This process terminates at S nk , at which point we have a set of n linearly independent vectors in R n , and since we only added vectors to S, S ⊂ S nk and we have extended S to be a basis for R n . Problem 2. Let u 1 = ± 2 1 ² ,u 2 = ± 4 3 ² ,v 1 = ±3 1 ² ,v 2 = ± 25 ² a) Find the transition matrix from [ v 1 ,v 2 ] to [ u 1 ,u 2 ]. S = U1 V = 1 2 ± 341 2 ²±3 2 15 ² = 1 2 ±13 26 512 ² b) If x = 3 v 14 v 2 = ± 34 ² V , determine the coordinates of x with respect to [ u 1 ,u 2 ]. x U = Sx V = 1 2 ±13 26 512 ²± 34 ² = 1 2 ±143 63 ² 1...
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 Spring '10
 PANTANO
 Linear Algebra, Vectors, basis, Euclidean space, linearly independent vectors

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