# If the number of equations in a linear system exceeds the number of unknowns, then the system must be inconsistent - FALSE. Linear Algebra

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)

• The statement in the title is false. – user296602 Jan 2 '16 at 20:53
• This was from my textbook, I added the reference. Yea I think it may be wrong as well.. – Mohit A. Jan 2 '16 at 20:56
• 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? – Rory Daulton Jan 2 '16 at 20:57
• Am i not reading the question properly? Let me change the title to match exactly what the book is saying – Mohit A. Jan 2 '16 at 20:58
• Yes, by Gaussian Elimination. The example you provided we have more variables than equations, the question is asking for more equations than variables – 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.