The system of equation x + y + z = 2, 3x − y + 2z = 6 and 3x + y + z = −18 has

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(a) a unique solution The given system of equations can be written in matrix form as follows: \begin{bmatrix}1 & 1 & 1 \ 3 & - 1 & 2 \ 3 & 1 & 1\end{bmatrix}\begin{bmatrix}x \ y \ z\end{bmatrix} = \begin{bmatrix}2 \ 6 \ - 18\end{bmatrix} AX = B Here, A = \begin{bmatrix}1 & 1 & 1 \ 3 & - 1 & 2 \ 3 & 1 & 1\end{bmatrix}, X = \begin{bmatrix}x \ y \ z\end{bmatrix}	ext{ and }B = \begin{bmatrix}2 \ 6 \ - 18\end{bmatrix} \left| A ight|=1 \left( - 1 - 2 ight) - 1\left( 3 - 6 ight) + 1\left( 3 + 3 ight) = - 3 + 3 + 6 = 6
eq0 So, the given system of equations has a unique solution.

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