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{"ops":[{"insert":"In each part of Exercises 21\u201322, find the eigenvalues and the\ncorresponding eigenspaces of the stated matrix operator on R3.\nRefer to the tables in Section 4.9 and use geometric reasoning to\nfind the answers. No computations are needed.\n21. (a) Reflection about the xy-plane.\n(b) Orthogonal projection onto the xz-plane.\n(c) Counterclockwise rotation about the positive x-axis\nthrough an angle of 90\u25e6.\n(d) Contraction with factor k (0 \u2264 k < 1).\n22. (a) Reflection about the xz-plane.\n(b) Orthogonal projection onto the yz-plane.\n(c) Counterclockwise rotation about the positive y-axis\nthrough an angle of 180\u25e6.\n(d) Dilation with factor\n"}]}
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