Exercise 1.4.30

Avg difficulty 3.0

Consider the system $-5x+2y-z=0$ and $-5x-2y-z=0$ . Both equations equal zero and so $-5x+2y-z=-5x-2y-z$ which is equivalent to $y=0$ . Does it follow that $x$ and $z$ can equal anything? Notice that when $x=1$ , $z=-4$ , and $y=0$ are plugged in to the equations, the equations do not equal $0$ . Why?

Selinger, Matrix Theory and Linear Algebra, Systems of linear equations, Gaussian elimination, Exercise 1.4.30

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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.