- #1
Icheb
- 42
- 0
I have a square triangular matrix with [tex]d_{ij} = 0[/tex] for all [tex]1 \le j < i \le n[/tex]. Now I have to prove that this matrix is only then invertible when [tex]d_{ii} \ne 0[/tex] for all [tex]1 \le i \le n[/tex].
From what I know a matrix is only then invertible when its determinant does not equal 0. I also think that the determinant of a triangular matrix is dependent on the product of the elements of the main diagonal and if that's true, I'd have the proof. However this is also where I'm stuck since I don't know how to prove that. Could someone help me there?
From what I know a matrix is only then invertible when its determinant does not equal 0. I also think that the determinant of a triangular matrix is dependent on the product of the elements of the main diagonal and if that's true, I'd have the proof. However this is also where I'm stuck since I don't know how to prove that. Could someone help me there?