Let be a positive integer and _r = vmatrix r^2+r & r+1 & r-2 2r^2+3r-1 & 3r & 3r-3…

MATHEMATICS · Subjective · CBSE · Mathematics · Determinants · Determinants

Problem

Let

n

be a positive integer and

\Delta_r = \begin{vmatrix} r^2+r & r+1 & r-2 \\ 2r^2+3r-1 & 3r & 3r-3 \\ r^2+2r+3 & 2r-1 & 2r-1 \end{vmatrix} \text{ and}

\sum_{r=1}^{n} \Delta_r = an^2 + bn + c, \text{ find the value of } a+b+c.