Corollary 1.2.1 Proof

Prove Corollary 1.2.1 from the textbook using the hint given there. Pn Pi=1 Pn Pn Corollary 1.2.1 states that i=1 j=1 xi,j = j=1 i=j xi,j . The hint given in the textbook tells us to “consider data values xi,j , where i and j both take values Pn from Pm1 to n and Pm where Pn xi,j = 0 when j > i ” and to “then apply Proposition 1.2.1,” which states that i=1 1 xi,j = j=1 i=1 xi,j . Translating the hint, we have the following n × n array: x1,1 x2,1 x3,1 .. .

x2,2 x3,2 .. .

x3,1 .. .

xn,1

xn,2

xn,3

1

..

. ...

xn,n