Log In Start studying!

Select your language

Suggested languages for you:
Answers without the blur. Sign up and see all textbooks for free! Illustration


Linear Algebra With Applications
Found in: Page 323
Linear Algebra With Applications

Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

Answers without the blur.

Just sign up for free and you're in.


Short Answer

Arguing geometrically, find all eigenvectors and eigenvalues of the linear transformations in Exercises 15 through 22. In each case, find an eigenbasis if you can, and thus determine whether the given transformation is diagonalizable.

Rotation through an angle of 180° in R2.

So, A is diagonalizable.

See the step by step solution

Step by Step Solution

Step 1: Definition of diagonalizable

A matrix is known as diagonalizable if it can be written in the form of A=PDP-1.

Step 2: Checking whether the matrix diagonalizable

Rotation through an angle of 180° will turn any vector v into -v , so role="math" localid="1659525298008" A=-l2, and all vectors vR2are eigenvectors of A with the corresponding eigenvalue being λ=-1. The very fact that A=-l2 is already diagonal proves that it's diagonalizable.

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free
94% of StudySmarter users get better grades.