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Exercise 1.4.4

Avg difficulty 3.0

Consider the following augmented matrix in which ∗\ast denotes an arbitrary number and ■\blacksquare denotes a non-zero number. Determine whether the given augmented matrix is consistent. If consistent, is the solution unique?

[■∗∗∗∗∗0■∗∗0∗0000■00000∗■]\left[\begin{array}{ccccc|c}\blacksquare&\ast&\ast&\ast&\ast&\ast\\ 0&\blacksquare&\ast&\ast&0&\ast\\ 0&0&0&0&\blacksquare&0\\ 0&0&0&0&\ast&\blacksquare\end{array}\right]

Selinger, Matrix Theory and Linear Algebra, Systems of linear equations, Gaussian elimination, Exercise 1.4.4

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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.