Answer to Question #238047 in Linear Algebra for lindokuhle

Question

In each part of Exercises 21–22, find the eigenvalues and the

corresponding eigenspaces of the stated matrix operator on R3.

Refer to the tables in Section 4.9 and use geometric reasoning to

find the answers. No computations are needed.

21. (a) Reflection about the xy-plane.

(b) Orthogonal projection onto the xz-plane.

(c) Counterclockwise rotation about the positive x-axis

through an angle of 90◦.

(d) Contraction with factor k (0 ≤ k < 1).

22. (a) Reflection about the xz-plane.

(b) Orthogonal projection onto the yz-plane.

(c) Counterclockwise rotation about the positive y-axis

through an angle of 180◦.

(d) Dilation with factor

Answer 1

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