In Exercises, use Example to list the eigenvalues of A. In

Chapter 5, Problem 8E

(choose chapter or problem)

Get Unlimited 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.

\(\left[\begin{array}{rr}\sqrt{3} & 3 \\ -3 & \sqrt{3}\end{array}\right]\)

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.

Add to cart


Study Tools You Might Need

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back