My Math Forum determinant n by n matrix

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 January 6th, 2016, 07:22 AM #1 Newbie   Joined: Jun 2012 Posts: 12 Thanks: 0 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)
January 6th, 2016, 09:12 AM   #2
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Quote:
 Originally Posted by wortel 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?

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