[Question 2014a02] Fudan Higher Algebra I (Class 14) Monday question (fourth teaching week)

[Question 2014a02]Evaluate the value of the following \ (n \) Order Determinant, where \ (a_ I \ NEQ 0 \, (I = 1, 2, \ cdots, n )\):

\ [D_n =\begin {vmatrix} 0 & a_1 + A_2 & \ cdots & a_1 + A _ {n-1} & a_1 + a_n \ A_2 + A_1 & 0 & \ cdots & a_2 + A _ {n-1} & A_2 + a_n \ vdots & \ vdots \ A _ {n-1} + A_1 & _{ n-1} + A_2 & \ cdots & 0 & A _ {n-1} + a_n \ a_n + A_1 & a_n + A_2 & \ cdots & a_n + A _ {n-1} & 0 \ end {vmatrix }. \]

NoteAt this stage, try not to use the descending formula of the matrix. We recommend that you use the progressive method and split method to simplify the calculation.

[Question 2014a02] Fudan Higher Algebra I (Class 14) Monday question (fourth teaching week)