If (x) = vmatrix + x & + x & + x + x & + x & + x + x & + x & + x vmatrix show that and

MATHEMATICS · Subjective · CBSE · Mathematics · Determinants · Determinants

Problem

If Δ(x)=∣α+xθ+xλ+xβ+xϕ+xμ+xγ+xψ+xγ+x∣\text{If } \Delta(x) = \begin{vmatrix} \alpha + x & \theta + x & \lambda + x \\ \beta + x & \phi + x & \mu + x \\ \gamma + x & \psi + x & \gamma + x \end{vmatrix} show that Δ′′(x)=0\Delta''(x) = 0 and Δ(x)=Δ(0)+Sx\Delta(x) = \Delta(0) + Sx , where SS denotes the sum of all the cofactors of all elements in Δ(0)\Delta(0) and dash denotes the derivative.

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