Understanding and Calculating Matrix Determinants - Step by Step Guide

[encomes]

How can I get the determinant of this matrix?

1-n 1 ...1 1
1 1-n ...1 1
. . . .
. . . .
1 1 ... 1 1-n

I think that the answer is 0 but... why?

Thank you.

 

[HallsofIvy]

How can I get the determinant of this matrix?

1-n 1 ...1 1
1 1-n ...1 1
. . . .
. . . .
1 1 ... 1 1-n

I think that the answer is 0 but... why?

Thank you.

Is "n" here the order of the matrix? If so then, by a row reduction to diagonal or triangular form, you can show that the last row becomes all "0"s.

 

[encomes]

Thx for your reply, but I can't see how u get to this solution.. Can u show me the process?
Thanks again!

 

[HallsofIvy]

Try this: add all of the other rows to the first row. What do you get?

(Try it with n= 2, 3, and 4 first.)

 

[encomes]

Alright, so, if I have a determinant with n=4, i add all the rows to the first and i get (4-n +4-n +4-n +4-n), so, it's 0.

Is there any other process?

Thank you.