Rank, Co-factor matrices.

  • Thread starter harvesl
  • Start date
  • #1
9
0

Homework Statement



Let A be an n x n matrix where [itex]n \geq 2[/itex]. Show that [itex]A^{\alpha} = 0[/itex] (where [itex]A^{\alpha}[/itex] is the cofactor matrix and 0 here denotes the zero matrix, whose entries are the number 0) if and only if [itex]rankA \leq n-2[/itex]



Homework Equations





The Attempt at a Solution


No idea where to start with this, it's just an additional question in the lecture notes which I haven't gone through in tutorial. Thanks.
 

Answers and Replies

  • #2
312
0
The cofactor matrix is obtained by deleting rows and columns and taking the determinant. Given the rank<=n-2, what about the rank after deletion? What about the determinant?
 

Related Threads on Rank, Co-factor matrices.

  • Last Post
Replies
0
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
5
Views
7K
  • Last Post
Replies
1
Views
672
  • Last Post
Replies
7
Views
1K
Replies
3
Views
3K
Replies
2
Views
3K
Replies
1
Views
17K
Replies
1
Views
11K
  • Last Post
Replies
2
Views
2K
Top