(D) matrix $A$ has no inverse if and only if its determinant is zero,i.e.,$\det(A) = 0$. Calculating the determinant of matrix $A$: $\det(A) = 1(x - 1

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(D) matrix $A$ has no inverse if and only if its determinant is zero,i.e.,$\det(A) = 0$. Calculating the determinant of matrix $A$: $\det(A) = 1(x - 1) - 1(1 - x) + x(1 - x^2) = 0$ $x - 1 - 1 + x + x - x^3 = 0$ $-x^3 + 3x - 2 = 0$ $x^3 - 3x + 2 = 0$ Factoring the cubic equation: $(x - 1)(x^2 + x - 2) = 0$ $(x - 1)(x - 1)(x + 2) = 0$ $(x - 1)^2(x + 2) = 0$ The values of $x$ are $1$ and $-2$. The distinct values of $x$ are $1$ and $-2$. The sum of these distinct values is $1 + (-2) = -1$.

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

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The sum of the distinct values of $x$ for which the matrix $A=\begin{bmatrix} 1 & 1 & x \\ 1 & x & 1 \\ x & 1 & 1 \end{bmatrix}$ has no inverse,is

AP EAMCET 2023 All AP EAMCET

A
$4$
B
$3$
C
$2$
D
$-1$

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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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The sum of the distinct values of $x$ for which the matrix $A=\begin{bmatrix} 1 & 1 & x \\ 1 & x & 1 \\ x & 1 & 1 \end{bmatrix}$ has no inverse,is

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