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Back to Gaussian elimination

Exercise 1.4.16

Avg difficulty 3.0

Find the general solution of the system whose augmented matrix is

(a) [120213421021](b) [120220113213](c) [11011042](a)~{}\left[\begin{array}{rrr|r}1&2&0&2\\ 1&3&4&2\\ 1&0&2&1\end{array}\right]\quad(b)~{}\left[\begin{array}{rrr|r}1&2&0&2\\ 2&0&1&1\\ 3&2&1&3\end{array}\right]\quad(c)~{}\left[\begin{array}{rrr|r}1&1&0&1\\ 1&0&4&2\end{array}\right] (d) [102112010121120013101022](e) [1021120101210200131−12220](d)~{}\left[\begin{array}{rrrrr|r}1&0&2&1&1&2\\ 0&1&0&1&2&1\\ 1&2&0&0&1&3\\ 1&0&1&0&2&2\end{array}\right]\quad(e)~{}\left[\begin{array}{rrrrr|r}1&0&2&1&1&2\\ 0&1&0&1&2&1\\ 0&2&0&0&1&3\\ 1&-1&2&2&2&0\end{array}\right]

Selinger, Matrix Theory and Linear Algebra, Systems of linear equations, Gaussian elimination, Exercise 1.4.16

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Adapted from Matrix Theory and Linear Algebra © 2017–2026 Peter Selinger, Lyryx Learning, and Ken Kuttler. Licensed under CC BY 4.0. Source: Matrix Theory and Linear Algebra. Imported at revision d74bc3a.