Let A be a square matrix defined by ( A = egin{pmatrix}-2&-1&-5\ 2&2&3\ 4&2&2end{pmatrix} ) (a)...

70.2K

Verified Solution

Question

Advance Math

Let A be a square matrix defined by ( A = egin{pmatrix}-2&-1&-5\ 2&2&3\ 4&2&2end{pmatrix} )
(a) Find the characteristic polynomial of A.
(b) Find the eigenvalues and eigenspaces of A.
(c) Show that A is not diagonalizable, but it is triangularizable, then triangularize A.
(d) Find the three real sequences ( (a)_n, (b)_n ,(c)_n ) satisfying.
( egin{cases}a_{n+1}=-2a_n-b_n-5c_n hspace{2mm},a_0=1 & quad \b_{n+1}=2a_n+2b_n+3c_n hspace{2mm}, b_0=0 & quad \c_{n+1}=4a_n+2b_n+6c_n hspace{2mm},c_0=1 & quadend{cases} )

Answer & Explanation Solved by verified expert

4.5 Ratings (980 Votes)

Solution a Find the characteristic polynomial of A we have A eginpmatrix215 223 422endpmatrix implies Plambdalambda36lambda212lambda8igglambda2igg3 Thus Plambdaigglambda2igg3 b Find the eigenvalues and eigenspaces of A lambda in spA iff Plambda0implies lambda 2 hspace2mmwith hspace2mm am23 A2Ieginpmatrix415 203 424endpmatrixsim eginpmatrix203 011 000endpmatrix Let 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}-2&-1&-5\ 2&2&3\ 4&2&2end{pmatrix} ) (a)...