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(Reflections and projections) (a) Let T : R 3 → R 3 be the transformation from the conceptual problems for Chapter 4: T(x) = 1 3 −1 −2 2 −2 2 1 2 1 2 x. Determine the eigenvalues of T, and find a basis for each eigenspace. (b) Remember that T is supposed to be ‘reflection across a plane S’. Explain what the eigenvalues and eigenvectors from (a) mean geometrically. What is their relationship to S? Why does it make sense for the eigenvalues to be 1 and −1?
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(Reflections and projections) (a) Let T : R 3 → R 3 be the transformation from the conceptual proble...
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