Matrix!

Algebra Level 5

Δ x = x x 2 2 x + 1 2 x + 1 2 x 2 1 4 x + 2 x 2 + x x 3 + x 2 2 x 2 + 3 x + 2 \Delta_{x} = \begin{vmatrix} x & x^2 & 2x+1 \\ 2x+1 & 2x^2-1 & 4x+2 \\ x^2+x & x^3+x^2 & 2x^2+3x+2 \end{vmatrix} Then find value of : x = 1 10 Δ x \displaystyle\sum_{x=1}^{10} \Delta_x


The answer is -440.

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2 solutions

Akhilesh Vibhute
Jan 16, 2016

D=-x-x^2 So D = -440

Perform the following row operations: Replace R3 by R3-R1. After that replace R2 by R2-2R1. After that replace R3 by R3- x x R1. After that expand the determinant along the third row to get the value of determinant as x -x - x 2 x^2 . After that we get the value of summation as 440 -440 .

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