Let A be a square matrix defined by$ A =\begin{pmatrix}2&-3&1\\ 1&-2&1\\ 1&-3&2\end{pmatrix} $ (a) Find the...

70.2K

Verified Solution

Question

Advance Math

Let A be a square matrix defined by$ A =\begin{pmatrix}2&-3&1\\ 1&-2&1\\ 1&-3&2\end{pmatrix} $
(a) Find the characteristic polynomial of A.
(b) Show that A is diagonalizable then diagonalize it.
(c) Write $A^n$ \hspace{2mm} in term of n.
Â
Â

Answer & Explanation Solved by verified expert

4.1 Ratings (476 Votes)

Solution a Find the characteristic polynomial of A we have A beginpmatrix231 121 132endpmatrix implies PlambdaAlambda Ibigg1bigg3bigglambda3S1lambda2S2lambdaS3bigg bullet hspace2mmS12222 bullet hspace2mmS2beginvmatrix21 32endvmatrixbeginvmatrix11 12endvmatrixbeginvmatrix12 12endvmatrix bigg43biggbigg21biggbigg32bigg1 bullet hspace2mmS3beginvmatrix231 121 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\( A =\begin{pmatrix}2&-3&1\\ 1&-2&1\\ 1&-3&2\end{pmatrix} \) (a) Find the...

70.2K

Verified Solution

Question

Advance Math

Let A be a square matrix defined by\( A =\begin{pmatrix}2&-3&1\\ 1&-2&1\\ 1&-3&2\end{pmatrix} \)
(a) Find the characteristic polynomial of A.
(b) Show that A is diagonalizable then diagonalize it.
(c) Write $A^n$ \hspace{2mm} in term of n.
Â
Â

Answer & Explanation Solved by verified expert

Get Answers to Unlimited Questions

Membership Benefits:

Other questions asked by students

Let A be a square matrix defined by\( A =\begin{pmatrix}2&-3&1\\ 1&-2&1\\ 1&-3&2\end{pmatrix} \) (a) Find the...

70.2K

Verified Solution

Question

Advance Math

Let A be a square matrix defined by\( A =\begin{pmatrix}2&-3&1\\ 1&-2&1\\ 1&-3&2\end{pmatrix} \)(a) Find the characteristic polynomial of A.(b) Show that A is diagonalizable then diagonalize it.(c) Write $A^n$ \hspace{2mm} in term of n.Â Â

Answer & Explanation Solved by verified expert

Get Answers to Unlimited Questions

Membership Benefits:

Other questions asked by students

Let A be a square matrix defined by\( A =\begin{pmatrix}2&-3&1\\ 1&-2&1\\ 1&-3&2\end{pmatrix} \)
(a) Find the characteristic polynomial of A.
(b) Show that A is diagonalizable then diagonalize it.
(c) Write $A^n$ \hspace{2mm} in term of n.
Â
Â