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January 6th, 2016, 07:22 AM   #1
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determinant n by n matrix

A n by n matrix A is given by that the (kth row, lth collumn) entry =k+l. What is the determinant of this matrix?

How to tackle this problem?
I know how to do it for a specific n but how to do it leaving n as a variable
for n= 3 I would get a matrix like below.

(1+1) (1+2) (1+3)
(2+1) (2+2) (2+3)
(3+1) (3+2) (3+3)
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January 6th, 2016, 09:12 AM   #2
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Quote:
Originally Posted by wortel View Post
I know how to do it for a specific n but how to do it leaving n as a variable
So what do you get for n = 2, 3, 4? Can you form a hypothesis for the general case? Have you tried applying standard transformations to rows or columns of the matrix?
Evgeny.Makarov is offline  
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