Label the following statements as true or false. Assume that the underlying vector
Chapter 6, Problem 1(choose chapter or problem)
Label the following statements as true or false. Assume that the underlying vector spaces are finite-dimensional real inner product spaces. (a) Any orthogonal operator is either a rotation or a re-flection. (b) The composite of any two rotations on a two-dimensional space is a rotation. (c) The composite e>f any two rotations on a three-dimensional space is a rotation. (d) The composite of any two rotations on a four-dimensional space is a rotation. (e) The ielentity operator is a rotation. (f) The composite of two reflections is a reflection. (g) Any orthogonal operator is a composite of rotations. (h) For any orthogonal operator T, if det(T) = 1, then T is a reflection, (i) Reflections always have eigenvalues, (j) Rotations always have eigenvalues.
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