• Support PF! Buy your school textbooks, materials and every day products Here!

Is there more than one way to prove this?

  • Thread starter pyroknife
  • Start date
  • #1
613
3
Suppose that A is an n × n matrix and u and v
are vectors in R^n. Show that if Au = Av and
u ≠ v, then A is not invertible.


This is the book's proof:
From the fact that Au = Av, we have A(u − v) = 0. If
A is invertible, then u − v = 0, that is, u = v, which
contradicts the statement that u = v.

Mine proof is, if A is invertible thus A^-1 exists
(A^-1)(Au)=(A^-1)(Av)
A^-1*A=I
→u=v
if u≠v then then the above does not hold, implying that A^-1 does not exist.
 

Answers and Replies

  • #2
gabbagabbahey
Homework Helper
Gold Member
5,002
6
Your proof looks fine to me :approve:
 

Related Threads on Is there more than one way to prove this?

Replies
6
Views
1K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
8
Views
2K
Replies
1
Views
1K
  • Last Post
Replies
10
Views
1K
Replies
6
Views
1K
Replies
2
Views
515
Replies
6
Views
3K
Replies
0
Views
1K
Replies
4
Views
1K
Top