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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 + x θ + x λ + x β + x ϕ + x μ + x γ + x ψ + x γ + 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} If Δ ( x ) = α + x β + x γ + x θ + x ϕ + x ψ + x λ + x μ + x γ + x
show that Δ ′ ′ ( x ) = 0 \Delta''(x) = 0 Δ ′′ ( x ) = 0 and Δ ( x ) = Δ ( 0 ) + S x \Delta(x) = \Delta(0) + Sx Δ ( x ) = Δ ( 0 ) + S x , where S S S denotes the sum of all the cofactors of all elements in Δ ( 0 ) \Delta(0) Δ ( 0 ) and dash denotes the derivative.
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