1 Which Of The Five Linear Transformations In Exercise Ii 1 On Page 19 Are Rigid Whi 879557

1.  Which of the five linear transformations in Exercise II.1 on page 19 are rigid? Which ones are both rigid and orientation-preserving?

2.  Let M = (u, v), that is, M =ho w that the linear transformation represented by the matrix M is rigid if and only ifand u · v = 0.Pr ove that if M represents a rigid transformation, then det (M) = ±1. A matrix M of the type in the previous exercise is called an orthonormal matrix.

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