Linear algebra question

  • Thread starter rabihtawil
  • Start date
  • #1
10
0

Homework Statement



question 1:
If A is a matrix satisfying 3A^2+6A-I=0, find the inverse of A.

question 2:
Let A be a 3x3 matrix with 4A = A^7. Find the possible values det A.

Homework Equations



none

The Attempt at a Solution



this was a very long homework about 17 questions, i solved the others but i got no clue where to start with these, any help is appreciated.

Best Regards.
 

Answers and Replies

  • #2
Hootenanny
Staff Emeritus
Science Advisor
Gold Member
9,621
7
question 1:
If A is a matrix satisfying 3A^2+6A-I=0, find the inverse of A.
HINT: Multiply through by A-1
question 2:
Let A be a 3x3 matrix with 4A = A^7. Find the possible values det A.
HINTs: det(4A) = 4ndet(A) for an nxn matrix. det(A7) = (det(A))7
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
41,847
966
Or, for question 1, note that [itex]3A^2+ 6A= I[/itex] so [itex](3A+ 6)A= I[/itex].
 

Related Threads on Linear algebra question

  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
20
Views
2K
  • Last Post
Replies
1
Views
852
  • Last Post
Replies
4
Views
918
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
4
Views
2K
Top