The system of simultaneous linear equations x | vedclass

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(D) First, we calculate the determinant $D$ of the coefficient matrix: $D = \begin{vmatrix} 1 & -2 & 3 \ 3 & 1 & -2 \ 2 & 3 & 1 \end{vmatrix} = 1(1

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unique solution having $z=\frac{1}{2}$

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(D) First, we calculate the determinant $D$ of the coefficient matrix: $D = \begin{vmatrix} 1 & -2 & 3 \ 3 & 1 & -2 \ 2 & 3 & 1 \end{vmatrix} = 1(1 - (-6)) - (-2)(3 - (-4)) + 3(9 - 2) = 1(7) + 2(7) + 3(7) = 7 + 14 + 21 = 42$. Since $D 
eq 0$, the system has a unique solution. To find $z$, we use Cramer's rule, $z = \frac{D_z}{D}$, where $D_z$ is the determinant obtained by replacing the third column with the constants: $D_z = \begin{vmatrix} 1 & -2 & 4 \ 3 & 1 & 7 \ 2 & 3 & 6 \end{vmatrix} = 1(6 - 21) - (-2)(18 - 14) + 4(9 - 2) = 1(-15) + 2(4) + 4(7) = -15 + 8 + 28 = 21$. Therefore, $z = \frac{21}{42} = \frac{1}{2}$.

The system of simultaneous linear equations $x-2y+3z=4$, $3x+y-2z=7$, and $2x+3y+z=6$ has

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