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Solved: In Exercises, use Example to list the eigenvalues
Chapter 5, Problem 9E(choose chapter or problem)
In Exercises 7–12, use Example 6 to list the eigenvalues of A. In each case, the transformation \(\mathbf{x} \mapsto A \mathbf{x}\) is the composition of a rotation and a scaling. Give the angle \(\varphi\) of the rotation, where \(-\pi<\varphi \leq \pi\), and give the scale factor r.
\(\left[\begin{array}{rr}-\sqrt{3} / 2 & 1 / 2 \\ -1 / 2 & -\sqrt{3} / 2\end{array}\right]\)
Questions & Answers
QUESTION:
In Exercises 7–12, use Example 6 to list the eigenvalues of A. In each case, the transformation \(\mathbf{x} \mapsto A \mathbf{x}\) is the composition of a rotation and a scaling. Give the angle \(\varphi\) of the rotation, where \(-\pi<\varphi \leq \pi\), and give the scale factor r.
\(\left[\begin{array}{rr}-\sqrt{3} / 2 & 1 / 2 \\ -1 / 2 & -\sqrt{3} / 2\end{array}\right]\)
ANSWER:Solution 9E
Step 1
