If a -2 b - c -1- then the value of begin vmatrix x-1 - x-2 - x-a x-2 - x-3 - x-b 1x-3 - x-4 - x-clend vmatrix - is A- xB- -1C- 1D- - x

The correct option is B 1x + 1 amp; x + 2 amp; x + a x + 2 amp; x + 3 amp; x + b x + 3 amp; x + 4 amp; x + c Apply the operation, ...

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Evaluation of a Determinant

If a -2 b + c...

Question

If a - 2b + c = 1, then the value of $∣ ∣ ∣ ∣ \begin{matrix} x + 1 & x + 2 & x + a x + 2 & x + 3 & x + b x + 3 & x + 4 & x + c \end{matrix} ∣ ∣ ∣ ∣ i s$

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a - 2 b + c = 1

f (x) = ∣ ∣ ∣ ∣ \begin{matrix} x + a & x + 2 & x + 1 x + b & x + 3 & x + 2 x + c & x + 4 & x + 3 \end{matrix} ∣ ∣ ∣ ∣,

f (x) = ∣ ∣ ∣ ∣ ∣ \begin{matrix} (x - a)^{4} & (x - a)^{3} & 1 (x - b)^{4} & (x - b)^{3} & 1 (x - c)^{4} & (x - c)^{3} & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣

f^{'} (x) = λ ∣ ∣ ∣ ∣ ∣ \begin{matrix} (x - a)^{4} & (x - a)^{2} & 1 (x - b)^{4} & (x - b)^{2} & 1 (x - c) & (x - c)^{2} & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣

λ

∣ ∣ ∣ ∣ ∣ \begin{matrix} x^{2} + x & x + 1 & x - 2 2 x^{2} + 3 x - 1 & 3 x & 3 x - 3 x^{2} + 2 x + 3 & 2 x - 1 & 2 x - 1 \end{matrix} ∣ ∣ ∣ ∣ ∣ = A x - 12

A

a x^{3} + b x^{2} + c x + d = ∣ ∣ ∣ ∣ \begin{matrix} x + 1 & 2 x & 3 x 2 x + 3 & x + 1 & x 2 - x & 3 x + 4 & 5 x - 1 \end{matrix} ∣ ∣ ∣ ∣

c ?

∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & x & x^{2} x & x^{2} & 1 x^{2} & 1 & x \end{matrix} ∣ ∣ ∣ ∣ ∣ = 3

∣ ∣ ∣ ∣ ∣ \begin{matrix} x^{3} - 1 & 0 & x - x^{4} 0 & x - x^{4} & x^{3} - 1 x - x^{4} & x^{3} - 1 & 0 \end{matrix} ∣ ∣ ∣ ∣ ∣

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