## Q8(b) from 2014 Final Winter

Exercise 8bAssume is an matrix with and has the property that each entry in the first row equals the sum of the entries in the column below it. Prove that .

You want to understand the wording of the question. What does it mean to say: “ each entry in the first row equals the sum of the entries in the column below it”. Here are some examples to get you started. This example has the property you want:

This example does not have the property you want:

because and .

To be a bit more formal, consider the following matrix:

We say that “the each entry in the first row is the sum of the entries in the column below it” if: and and . The left hand side of each equation is “an entry in the first row” and the right hand side is “the sum of the entries in the column below it”.

leave a comment