Show that the eigenvalues of an upper (or lower) triangular matrix are its diagonal

Problem 3

Show that the eigenvalues of an upper (or lower) triangular matrix are its diagonal entries.

                                                        Step by Step Solution

Step 1 of 2

Let  be an   upper triangular matrix. Then

Now,

It is known that the determinant of an upper triangular matrix is the product of its diagonal entries.

Therefore,  

Now,

Hence, eigenvalues of A are the diagonal entries.