Let the vectors (i, j, k) constitute an orthonormal basis. In terms of this basis, a general basis is: e₁ = 71 + 5ĵ + 5k, e₂ = 7î + 5j + 2k, e3 = 2î + 2) + 7k. Determine the dual basis (e¹, e², e³) of the above general basis in terms of (î, j, k). For vector A = 21 + 7ĵ + 5k, determine its contra-gradient components (A¹, A², A³) and co-gradient components (A1, A2, A3).

Let the vectors (i, j, k) constitute an orthonormal basis. In terms of this basis, a general basis is: e₁ = 71 + 5ĵ + 5k, e₂ = 7î + 5j + 2k, e3 = 2î + 2) + 7k. Determine the dual basis (e¹, e², e³) of the above general basis in terms of (î, j, k). For vector A = 21 + 7ĵ + 5k, determine its contra-gradient components (A¹, A², A³) and co-gradient components (A1, A2, A3).

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.1: Orthogonality In Rn

Problem 7EQ

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