Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. advance math
  3. let ( ain m_6(mathbb{r}) ) be an invertible matrix

Let ( Ain M_6(mathbb{R}) ) be an invertible matrix satisfies ( A^3-4A^2 + 3A =...

Free

70.2K

Verified Solution

Question

Advance Math

Let ( Ain M_6(mathbb{R}) ) be an invertible matrix satisfies ( A^3-4A^2 + 3A = 0 ) and ( tr(A) = 8. ) Find the characteristics polynomial of A.

 

Answer & Explanation Solved by verified expert
4.0 Ratings (598 Votes)

Solution

( Ain M_6(mathbb{R}) implies deg(Plambda) )

we have ( hspace{2mm}A^3-4A^2+3A=0 )

( iff Aigg(A^2-4A+3Iigg)=0 )

( iffigg(A-Iigg)igg(A-3Iigg)=0 )

Let ( f(lambda)=igg(lambda-Iigg)igg(lambda-3Iigg) ) Then ( f(A)=0 )

( implies P(lambda)=igg(lambda-1igg)^{n_1}igg(lambda-3igg)^{n_2} hspace{2mm} )where ( n_1+n_2=6 hspace{2mm}(1) )

we have ( tr(A)=8iff n_1(1)+n_2(3)=8 ) ( iff n_1+3n_2=8 )

from.(1) ( egin{cases} n_1+n_2=6 & quad\ n_1+3n_2=8 & quad end{cases} implies 2n_2=2implies n_2=1,n_1=5 )

 

Answer

Therefore. ( P(lambda)=igg(lambda-1igg)^5igg(lambda-3igg) )
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

Other questions asked by students

Q

Of the 93 participants in a drug trial who were given a new experimental treatment for?...

Basic Math
Q

Describe the mechanism used by a web application to prevent its session cookies from being used...

Programming
Q

Using 1.8*10^-5 for the Ka for acetic acid, along with the weight of sodium acetate and...

Chemistry
Q

Point out the differences between Non-persistent, 1-persistent and P-persistent modes of CSMA. Draw diagrams for each mode.

Electrical Engineering
Q

Qu 3. In class, we discussed two measures for theory of mind: the Sally/Ann task, and...

Psychology
Q

Microsoft Project Case: Shoreline Stadium Case The G&E Company is preparing a bid to build the new 47,000-seat...

General Management
Q

Containers of hazardous waste may be stored inside laboratory fume hoods when Select one Containers...

Biology
Q

The function h(t) gives the height of a rock thrown off the Golden Gate Bridge...

Basic Math
Q

R G B K Match each equation with a graph above 3 1 43 3...

Calculus
Q

Jennifer is single with no dependants. During the year she had the following amounts deducted...

Accounting
Q

Sarah and Jane formed a partnership with capital contributions of $180,000 and $126,000, respectively. Peter...

Accounting
Q

The purpose of a ceiling test under the full cost method is to: O insure...

Accounting