Name: Tamaswati

Who is asking: Student

Question:

How do I prove the assertion that "the determinant of an upper triangular matrix is the product of the diagonal entries" by mathematical induction? (Before I check this assertion for a few values of n how do I rephrase the assertion slightly so that n appears explicitly in the assertion?)

Hi Tamaswati,
What you want for n in this case is the "size" of the matrix. A matrix is a square array of numbers, say with n rows and n columns. We usually say an nxn matrix.

You can start the induction at n = 1. A 1x1 matrix has only one entry, call it **a**. The determinant has value **a** and this is also the product of the diaginal entries. If it bothers you to think of a 1x1 matrix ten start the induction at n = 2. An upper triangular 2x2 matrix is of the form

Its dertrminant is
axc - 0xb = axc
and the product of its diagonal entries is also axc.
Now try the inductive step.

Penny