Use an Inverse Matrix to Find the Solution to the System

question 137

Multiple Choice

Use an inverse matrix to find the solution to the system.
- $$\left\{ \begin{aligned}x _ { 1 } + x _ { 3 } + x _ { 4 } & = 4 \\x _ { 2 } + x _ { 3 } - x _ { 4 } & = 12 \\2 x _ { 1 } + 2 x _ { 2 } + x _ { 3 } - 3 x _ { 4 } & = 23 \\4 x _ { 2 } + 2 x _ { 4 } & = 6\end{aligned} \right.$$

• A) \(x _ { 1 } = 1 , x _ { 2 } = 4 , x _ { 3 } = 0 , x _ { 4 } = 1\)
• B) no solution
• C) \(x _ { 1 } = 2 , x _ { 2 } = 2 , x _ { 3 } = - 5 , x _ { 4 } = - 6\)
• D) \(x _ { 1 } = 1 , x _ { 2 } = 3 , x _ { 3 } = 6 , x _ { 4 } = - 3\)

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