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(A) The given system of linear equations is:$0x_1 + 1x_2 - 1x_3 = 1$$-1x_1 + 0x_2 + 2x_3 = -2$$1x_1 - 2x_2 + 0x_3 = 3$First,we calculate the determina

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(A) The given system of linear equations is:$0x_1 + 1x_2 - 1x_3 = 1$$-1x_1 + 0x_2 + 2x_3 = -2$$1x_1 - 2x_2 + 0x_3 = 3$First,we calculate the determinant $D$ of the coefficient matrix:$D = \begin{vmatrix} 0 & 1 & -1 \ -1 & 0 & 2 \ 1 & -2 & 0 \end{vmatrix} = 0(0 - (-4)) - 1(0 - 2) + (-1)(2 - 0) = 0 + 2 - 2 = 0$Since $D = 0$,the system is either inconsistent or has infinitely many solutions. We calculate $D_1$ by replacing the first column with the constants:$D_1 = \begin{vmatrix} 1 & 1 & -1 \ -2 & 0 & 2 \ 3 & -2 & 0 \end{vmatrix} = 1(0 - (-4)) - 1(0 - 6) + (-1)(4 - 0) = 4 + 6 - 4 = 6$Since $D = 0$ and $D_1 
eq 0$,the system of equations is inconsistent and has no solution.

The number of solutions of the following equations $x_2 - x_3 = 1$,$-x_1 + 2x_3 = -2$,$x_1 - 2x_2 = 3$ is

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