Consider the system of equations: x + y - az | vedclass

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(C) The determinant of the coefficient matrix is given by $\Delta = \begin{vmatrix} 1 & 1 & -a \ 2 & a & 1 \ a & 1 & -1 \end{vmatrix}$.Expanding alo

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For $a \in \{1, \frac{-1 \pm \sqrt{5}}{2}\}$,the system has no solution.

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(C) The determinant of the coefficient matrix is given by $\Delta = \begin{vmatrix} 1 & 1 & -a \ 2 & a & 1 \ a & 1 & -1 \end{vmatrix}$.Expanding along the first row: $\Delta = 1(-a - 1) - 1(-2 - a) - a(2 - a^2) = -a - 1 + 2 + a - 2a + a^3 = a^3 - 2a + 1$.Factoring the cubic expression: $\Delta = (a - 1)(a^2 + a - 1)$.The roots of $\Delta = 0$ are $a = 1$ and $a = \frac{-1 \pm \sqrt{5}}{2}$.For $a = 1$,the system becomes $x + y - z = 1$,$2x + y + z = 1$,$x + y - z = 2$. The first and third equations are contradictory $(1 
e 2)$,so there is no solution.For $a = \frac{-1 \pm \sqrt{5}}{2}$,$\Delta = 0$. By checking the augmented matrix,it is found that the system is inconsistent for these values as well.Thus,for all values where $\Delta = 0$,the system has no solution.

Consider the system of equations: $x + y - az = 1$; $2x + ay + z = 1$; $ax + y - z = 2$. Which of the following statements is correct?

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