Thread: Singular Matrix Proof

Prove that an nxn matrix of:
[1 2 3 .... n
n+1 n+2 n+3 .... 2n
2n+1 2n+2....3n
....
(n-1)(n+1)....n^2]
will always be singular.

(Sorry, I don't know how to use the math HTML, but basically saying a matrix like
[1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16])

Originally Posted by tommiegirl13

Prove that an nxn matrix of:
[1 2 3 .... n
n+1 n+2 n+3 .... 2n
2n+1 2n+2....3n
....
(n-1)(n+1)....n^2]
will always be singular.

(Sorry, I don't know how to use the math HTML, but basically saying a matrix like
[1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16])

I haven't worked out the details, but this seems to cry out for an induction proof.

-Dan

Using the elemental operations and we obtain two equal columns.


Fernando Revilla