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Year 12 Specialist (Unit 3 & 4) Further matrices

Augmented matrices and Gaussian elimination

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Question 1
196379
The system of linear equations \(x+2y-z=3\), \(2x-y+3z=8\) and \(-x+y+2z=1\) is written as an augmented matrix. Which augmented matrix represents this system?
A.
\(\left(\begin{array}{ccc|c}1 & 2 & -1 & 3 \\ 2 & -1 & 3 & 8 \\ -1 & 1 & 2 & 1\end{array}\right)\)
B.
\(\left(\begin{array}{ccc|c}1 & 2 & -1 & 3 \\ 2 & -1 & 3 & 8 \\ -1 & 1 & 2 & -1\end{array}\right)\)
C.
\(\left(\begin{array}{ccc|c}1 & 2 & 1 & 3 \\ 2 & 1 & 3 & 8 \\ 1 & 1 & 2 & 1\end{array}\right)\)
D.
\(\left(\begin{array}{ccc|c}1 & 2 & -1 & 3 \\ 2 & -1 & 8 & 3 \\ -1 & 1 & 1 & 2\end{array}\right)\)
\(\left(\begin{array}{ccc|c}1 & 2 & -1 & 3 \\ 2 & -1 & 3 & 8 \\ -1 & 1 & 2 & 1\end{array}\right)\)

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