Vbegin vmatrix 1 - 1 - 1111 - 1-x - 1111 - 1 - 1- yendvmatrix -1 A- 1B- 0C- xD- x y

The correct option is D xy1 amp; 1 amp; 1 1 amp; 1+x amp; 1 1 amp; 1 amp; 1+y = 0 amp; 0 amp; 1 x amp; x amp; 1 0 amp; y ...

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Properties of Determinants

Vbegin vmatri...

Question

$∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 1 & 1 + x & 1 1 & 1 & 1 + y \end{matrix} ∣ ∣ ∣ ∣ =$

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∣ ∣ ∣ ∣ \begin{matrix} 1 + x & 1 & 1 1 & 1 + y & 1 1 & 1 & 1 + z \end{matrix} ∣ ∣ ∣ ∣ =

P = ∣ ∣ ∣ \begin{matrix} x & 1 1 & x \end{matrix} ∣ ∣ ∣

Q = ∣ ∣ ∣ ∣ \begin{matrix} x & 1 & 1 1 & x & 1 1 & 1 & x \end{matrix} ∣ ∣ ∣ ∣,

\frac{d Q}{d x} =

∣ ∣ ∣ ∣ \begin{matrix} 1 + a & 1 & 1 1 & 1 + b & 1 1 & 1 & 1 + c \end{matrix} ∣ ∣ ∣ ∣ = a b c + b c + c a + a b

(i) A = [\begin{matrix} 1 + x & 7 \\ 3 - x & 8 \end{matrix}]

(ii) A = [\begin{matrix} x - 1 & 1 & 1 \\ 1 & x - 1 & 1 \\ 1 & 1 & x - 1 \end{matrix}]

A = [\begin{matrix} x - 1 & 1 & 1 \\ 1 & x - 1 & 1 \\ 1 & 1 & x - 1 \end{matrix}]

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