Let A be a square matrix defined by ( A =egin{pmatrix}-1&3&-1\ -3&5&-1\ -3&3&1end{pmatrix} ) (a) Find...

50.1K

Verified Solution

Question

Advance Math

Let A be a square matrix defined by ( A =egin{pmatrix}-1&3&-1\ -3&5&-1\ -3&3&1end{pmatrix} )
(a) Find the characteristic polynomial of A.
(b) Show that A is diagonalizable then diagonalize it.
(c) Write ( A^n ) in term of n.

Answer & Explanation Solved by verified expert

4.1 Ratings (539 Votes)

Solution a Find the characteristic polynomial of A we have A eginpmatrix131 351 331endpmatrix implies PlambdaAlambda Iigg1igg3igglambda3S1lambda2S2lambdaS3igg ullet hspace2mmS1trA1515 ullet hspace2mmS2eginvmatrix51 31endvmatrixeginvmatrix11 31endvmatrixeginvmatrix13 35endvmatrix8448 ullet hspace2mmS3Aigg599iggigg1539igg1394 so Plambdaigglambda35lambda28lambda4igglambdaigglambda1iggigglambda2igg2 b Show that A is diagonalizable then diagonalize it since See Answer

Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:

Unlimited Question Access with detailed Answers
Zin AI - 3 Million Words
10 Dall-E 3 Images
20 Plot Generations
Conversation with Dialogue Memory
No Ads, Ever!
Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!

Become a Member

Let A be a square matrix defined by ( A =egin{pmatrix}-1&3&-1\ -3&5&-1\ -3&3&1end{pmatrix} ) (a) Find...