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Unformatted text preview: orthogonal basis in the image of T . c) (10pt) Find (Ker T ) ⊥ and (Im T ) ⊥ . 4 Name 5 Name Problem 3 (30pt). The former secret agent is now a constructor. His company works in the Euclidean space R 3 . He has got a tool called the GramSchmidt orthogonalization and a basis { (1 , 1 , 1) , (2 , , 1) , (2 , 4 , 5) } of R 3 . Help him to construct an orthonormal basis of R 3 out of the given basis! 6 Name 7 Name Problem 4 (10pt). Let V be a ﬁnite dimensional inner product space. a) (3pt) Formulate the CauchySchwarz inequality b) (2pt) Formulate the Triangle inequality c) (2pt) Formulate the Pythagorean theorem d) (3pt) Which transformation of V is called orthogonal?...
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 Spring '09
 francis
 Linear Algebra, Algebra, orthogonal basis, Julia Viro, Euclidean space R3, Stony Brook University Mathematics Department, Linear Algebra MAT

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