Prove that an upper triangular nxn matrix is invertible if and only if all its diagonal entires are nonzero

Question

anonymous · Answer

If the upper triangular square matrix have at-least one diagonal element zero then it will be a singular which is a never invertible.

anonymous · Answer

ok, why would it be singular?

asnaseer · Answer

If a matrix M is invertible, then it implies that it's determinant is non-zero.
If this matrix is diagonal or upper triangular or lower triangular, then it's determinant is the product of the diagonal entries.

anonymous · Answer

Ah ok thanks, I'm looking at the proof for it now

asnaseer · Answer

this might help: http://en.wikipedia.org/wiki/Triangular_matrix

asnaseer · Answer

there's also a nice video on this here that might help you: http://www.youtube.com/watch?v=VX7K8iqoiRc

anonymous · Answer

thank you

asnaseer · Answer

yw