(D) Let $\Delta = \left| \begin{array}{ccc} -1 & 1 & 1 \\ 1 & -1 & 1 \\ 1 & 1 & -1 \end{array} \right|$.Applying the row operation $R_1 \to R_1 + R_2$

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(D) Let $\Delta = \left| \begin{array}{ccc} -1 & 1 & 1 \\ 1 & -1 & 1 \\ 1 & 1 & -1 \end{array} \right|$.Applying the row operation $R_1 \to R_1 + R_2$:$\Delta = \left| \begin{array}{ccc} 0 & 0 & 2 \\ 1 & -1 & 1 \\ 1 & 1 & -1 \end{array} \right|$.Now,expanding along the first row $(R_1)$:$\Delta = 0(1 - 1) - 0(-1 - 1) + 2(1 - (-1))$$\Delta = 2(1 + 1) = 2(2) = 4$.Therefore,the value of the determinant is $4$.

Class 12 Mathematics 3 and 4 .Determinants and Matrices Expansion of determinants, Solution of equation in the form of determinants and area of triangle and Equation of Line

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The value of the determinant $\left| \begin{array}{ccc} -1 & 1 & 1 \\ 1 & -1 & 1 \\ 1 & 1 & -1 \end{array} \right|$ is equal to

A
$-4$
B
$0$
C
$1$
D
$4$

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3 and 4 .Determinants and Matrices

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Expansion of determinants, Solution of equation in the form of determinants and area of triangle and Equation of Line

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MediumIIT 1982

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MediumTS EAMCET 2022

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The value of the determinant $\left| \begin{array}{ccc} -1 & 1 & 1 \\ 1 & -1 & 1 \\ 1 & 1 & -1 \end{array} \right|$ is equal to

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