cbadbe…: “Until a fair chord”

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The augmented matrix of a system of linear equations has been carried to the following by row operations. Solve the system.

\[\left [\begin{array}{cccccc|c} 1 & -2 & 0 & 2 & 0 & 1 & 1\\ 0 & 0 & 1 & 5 & 0 & -3 & -1\\ 0 & 0 & 0 & 0 & 1 & 6 & 1\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 \end{array}\right ]\]

\[(\answer {1-t-2s+2r}, r, \answer {-1+3t-5s}, s,\answer {1-6t}, t)\]

Source

[Nicholson] W. Keith Nicholson, Linear Algebra with Applications, Lyryx 2021, Open Edition, Problem 1.2.3 (b).