Math 1600A Section 2.2 Question31

$ \newcommand{\bmat}[1]{\left[\begin{array}{#1}} \newcommand{\emat}{\end{array}\right]} \newcommand{\coll}[2]{\bmat{r} #1 \\ #2 \emat} \newcommand{\colll}[3]{\bmat{r} #1 \\ #2 \\ #3 \emat} \newcommand{\red}[1]{{\color{red}#1}} \newcommand{\lra}[1]{\mbox{$\xrightarrow{#1}$}} \newcommand{\rank}{\textrm{rank}} \newcommand{\mystack}[2]{\genfrac{}{}{0}{0}{#1}{#2}} \newcommand{\mystackthree}[3]{\mystack{\mystack{#1}{#2}}{#3}} $
The solution to this question in the Solutions Manual says "From the beginning, we know that this system has infinitely many solutions ... because this system has 5 variables and only 3 equations they have to satisfy."

This is faulty logic. If the system is consistent, then it is true that it must have infinitely many solutions when there are more variables than equations, but it is also possible for the system to be inconsistent.

Someone also asked about how to do the row reduction. Click here for a hint:

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