From f4bf9fbcc0eb321a92d4521b870c0e9ae9299418 Mon Sep 17 00:00:00 2001
From: Drew Lewis <drew.lewis@gmail.com>
Date: Wed, 25 Feb 2026 15:03:22 +0000
Subject: [PATCH] Add check for nonemptiness to solution

---
 source/linear-algebra/exercises/outcomes/EV/EV3/template.xml | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

diff --git a/source/linear-algebra/exercises/outcomes/EV/EV3/template.xml b/source/linear-algebra/exercises/outcomes/EV/EV3/template.xml
index c75a325f3..2e1116ad8 100644
--- a/source/linear-algebra/exercises/outcomes/EV/EV3/template.xml
+++ b/source/linear-algebra/exercises/outcomes/EV/EV3/template.xml
@@ -82,7 +82,10 @@ Prove that <m>R</m> <em>is</em> a subspace.
         </content>
         <outtro>
             <p>
-First show that <m>R</m> is closed under
+                First note that <m>\vec{0} \in R</m>, so the set is nonempty.
+            </p>
+            <p>
+Next, show that <m>R</m> is closed under
 vector addition. Let <m>{{v}}\in R</m> so that
 <m>{{R_eq}}</m>, and let <m>{{valt}}\in R</m> so that
 <m>{{R_eq_alt}}</m>. Then use those assumptions to show