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45. Let {v, w} be an orthonormal basis for R², and let T: R2 → R² be the function defined by T(u) = (u • v cos 0 +u•w sin0)v +(-u•v sin0 +u•wcos 0)w. Prove that T is an orthogonal operator.

45. Let {v, w} be an orthonormal basis for R², and let T: R2 → R² be the function defined by T(u) = (u • v cos 0 +u•w sin0)v +(-u•v sin0 +u•wcos 0)w. Prove that T is an orthogonal operator.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.3: Orthonormal Bases:gram-schmidt Process
Problem 17E: Complete Example 2 by verifying that {1,x,x2,x3} is an orthonormal basis for P3 with the inner...
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45. Let {v, w} be an orthonormal basis for R², and let T: R² → R² be the function defined by T (u) = (u • v cos 0 +u•wsin0)v +(-u•v sin0 +u•w cos 0)w. Prove that T is an orthogonal operator.
Transcribed Image Text:45. Let {v, w} be an orthonormal basis for R², and let T: R² → R² be the function defined by T (u) = (u • v cos 0 +u•wsin0)v +(-u•v sin0 +u•w cos 0)w. Prove that T is an orthogonal operator.
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