Suppose that U is a linear transformation from R" into R" that is isometric, meaning that ||Ux|| = ||x|| for all x E R". (a) Prove that (Ux,Uy) = (x,y) for all x, y E R". (b) If {v1,…,vk} is an orthonormal set in R", show that {Uv1,...,Uvg} is also orthonormal.

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.