- #1

TomMe

- 51

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Hello all.

I'm stuck with this excercise that is asking me to proof that the determinant of the nxn matrix with a's on the diagonal and everywhere else 1's equals to:

|A| = (a + n - 1).(a-1)^(n-1)

So the matrix should look something like:

[a 1 1.. 1]

[1 a 1.. 1]

[: ... :]

[1 ..1 1 a]

I started subtracting row n-1 from row n, row n-2 from row n-1 and so on. But this gives me a matrix with a bidiagonal part (if that's the correct term, probably not!) under the first row. This looks needlessly complicated, and I don't know how to go from there. Maybe I did it the wrong way..

I would appreciate any help.

I'm stuck with this excercise that is asking me to proof that the determinant of the nxn matrix with a's on the diagonal and everywhere else 1's equals to:

|A| = (a + n - 1).(a-1)^(n-1)

So the matrix should look something like:

[a 1 1.. 1]

[1 a 1.. 1]

[: ... :]

[1 ..1 1 a]

I started subtracting row n-1 from row n, row n-2 from row n-1 and so on. But this gives me a matrix with a bidiagonal part (if that's the correct term, probably not!) under the first row. This looks needlessly complicated, and I don't know how to go from there. Maybe I did it the wrong way..

I would appreciate any help.

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