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Unformatted text preview: { A v 1 ,...,A v n } is a basis for R n . b. Let T be a linear transformation on R n and let e 1 , e 2 ,..., e n be the standard basis. Let A be the standard matrix of T . Prove that if T ( e 1 ) ,T ( e 2 ) ,...,T ( e n ) is a basis of R n then A is invertible. 7) Let B = 1 2 3 41246 4 8 a. Find a basis for the row space of A . b. Find a basis for the column space of A . c. Find a basis for the null space of A . d. What is the rank of A ? 8) a. Let H and K be subspaces of vector space V . The intersection of H and K , written as H K , is the set of v in V that belong to both H and K . Show that H K is a subspace of V . b. Give an example to show that the union of two subspaces is not, in general, a subspace. Justify your answer. 3...
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 Winter '10
 AMIR

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