I don't understand how this statement is FALSE. What if a matrix resulted in a row which led us to row 0x2 = 9, which would tell us that the plane or vector is parallel?

Thanks in advance for clearing up my confusion.

Reference : This was from my linear algebra textbook. Elementary Linear Algebra Tenth Edition by Howard Anton and Chris Rorres.

Chapter 1.1 True False exercise (e)

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    $\begingroup$ The statement in the title is false. $\endgroup$ – user296602 Jan 2 '16 at 20:53
  • $\begingroup$ This was from my textbook, I added the reference. Yea I think it may be wrong as well.. $\endgroup$ – Mohit A. Jan 2 '16 at 20:56
  • $\begingroup$ The system $x+y+z=1,\ x+y+z=2$ is inconsistent. And what do you mean by "a matrix resulted in a row which led us to row 0x2 = 9": do you mean during Gaussian elimination? $\endgroup$ – Rory Daulton Jan 2 '16 at 20:57
  • $\begingroup$ Am i not reading the question properly? Let me change the title to match exactly what the book is saying $\endgroup$ – Mohit A. Jan 2 '16 at 20:58
  • $\begingroup$ Yes, by Gaussian Elimination. The example you provided we have more variables than equations, the question is asking for more equations than variables $\endgroup$ – Mohit A. Jan 2 '16 at 21:04

The key word here is must. I.e., the statement claims that every system of linear equations with more equations than unknowns is inconsistent. That’s false. For example, the system $$\begin{align} x &= 1 \\ 2x &= 2 \end{align}$$ has two equations and one unknown, but is clearly consistent.

  • $\begingroup$ Oh man, that definitely works. Wow what a way to confuse what they are trying to say. Thanks! $\endgroup$ – Mohit A. Jan 2 '16 at 22:23

The statement in the title isn't necessarily true. It's entirely possible for a system to be inconsistent even though the number of equations is greater than the number of variable.

Maybe the statement was taken out of context?

  • $\begingroup$ I changed the title, to exactly what the question says. $\endgroup$ – Mohit A. Jan 2 '16 at 21:14

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