I am trying to solve this problem with no luck. I am supposed to prove that the determinant detA:
is divisible by the arithmetic formula:
I've tried separating the determinant by using the characteristic I know regarding determinants, especially trying to write the determinant as a sum of the coefficients in the last row (each determinant in the sum has only one coefficient in the last row that is not equal 0), but I haven't been able to prove the statement with this method.
Help would be much appreciated!
HINT: Add all the lines to the last one, meaning: $$\sum_{i=1}^{n-1} C_i\to C_n$$ which is a valid linear transformation.