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The inner product in V is defined according to the formula (u, v) 1V₂ - U₂v₁ +2u₂v₂. Let u (4, 1) and v = (2,3). i. Show that u and v form an orthogonal basis in the inner product space Use this basis to find an orthonormal basis by normalizing each vector. ii. Use the inner product defined in part b) to express the vector (1,1). as a linear combination of the orthonormal basis vectors obtained in part i. W: =

The inner product in V is defined according to the formula (u, v) 1V₂ - U₂v₁ +2u₂v₂. Let u (4, 1) and v = (2,3). i. Show that u and v form an orthogonal basis in the inner product space Use this basis to find an orthonormal basis by normalizing each vector. ii. Use the inner product defined in part b) to express the vector (1,1). as a linear combination of the orthonormal basis vectors obtained in part i. W: =

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.1: Orthogonality In Rn
Problem 34EQ
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The inner product in V is defined according to the formula (u, v) 1V2 - U₂v₁ + 2U₂V₂. Let u (4,1) and v = (2,3). i. Show that u and v form an orthogonal basis in the inner product space Use this basis to find an orthonormal basis by normalizing each vector. 11. Use the inner product defined in part b) to express the vector (1,1). as a linear combination of the orthonormal basis vectors obtained in part i. W: =
Transcribed Image Text:The inner product in V is defined according to the formula (u, v) 1V2 - U₂v₁ + 2U₂V₂. Let u (4,1) and v = (2,3). i. Show that u and v form an orthogonal basis in the inner product space Use this basis to find an orthonormal basis by normalizing each vector. 11. Use the inner product defined in part b) to express the vector (1,1). as a linear combination of the orthonormal basis vectors obtained in part i. W: =
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