Write the system of linear equations as a matrix equation, AX = B.

\left\{ \begin{aligned}x _ { 1 } - 3 x _ { 2 } + 2 x _ { 3 } & = 18 \\- x _ { 1 } + 3 x _ { 2 } - x _ { 3 } & = 18 \\3 x _ { 1 } - 3 x _ { 2 } + 3 x _ { 3 } & = 18\end{aligned} \right.

\left[ \begin{array} { l l l } 1 & 3 & 2 \\1 & 3 & 1 \\3 & 3 & 3\end{array} \right] \left[ \begin{array} { l } x _ { 1 } \\x _ { 2 } \\x _ { 3 }\end{array} \right] = \left[ \begin{array} { l } 18 \\18 \\18\end{array} \right]

\left[ \begin{array} { c c c } 1 & - 3 & 2 \\- 1 & 3 & - 1 \\3 & - 3 & 3\end{array} \right] \left[ \begin{array} { l } x _ { 1 } \\x _ { 2 } \\x _ { 3 }\end{array} \right] = \left[ \begin{array} { l } - 18 \\- 18 \\- 18\end{array} \right]

\left[ \begin{array} { c c c } 1 & - 3 & 2 \\- 1 & 3 & - 1 \\3 & - 3 & 3\end{array} \right] \left[ \begin{array} { l } x _ { 1 } \\x _ { 2 } \\x _ { 3 }\end{array} \right] = \left[ \begin{array} { l } 18 \\18 \\18\end{array} \right]

\left[ \begin{array} { c c c } 1 & - 1 & 3 \\- 3 & 3 & 3 \\2 & - 1 & 3\end{array} \right] \left[ \begin{array} { l } x _ { 1 } \\x _ { 2 } \\x _ { 3 }\end{array} \right] = \left[ \begin{array} { l } 18 \\18 \\18\end{array} \right]

\left[ \begin{array} { c c c } 1 & - 3 & 2 \\- 1 & 3 & - 1 \\3 & - 3 & 3\end{array} \right] \left[ \begin{array} { c } - x _ { 1 } \\- x _ { 2 } \\- x _ { 3 }\end{array} \right] = \left[ \begin{array} { l } 18 \\18 \\18\end{array} \right]

Use Cramer's Rule to Solve (If Possible) the System of Equations

Multiple Choice