Solution Found!
In Exercises, use Example to list the eigenvalues of A. In
Chapter 5, Problem 8E(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.
\(\left[\begin{array}{rr}\sqrt{3} & 3 \\ -3 & \sqrt{3}\end{array}\right]\)
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.
\(\left[\begin{array}{rr}\sqrt{3} & 3 \\ -3 & \sqrt{3}\end{array}\right]\)
ANSWER:Solution 8E
Step 1
Consider the following matrix:
To find the Eigen value of, the formula is:
Here,
Thus, the Eigen value is.