From 4e3124e3e5950fd61922535e3f9dd1809314e421 Mon Sep 17 00:00:00 2001
From: Steven Clontz <steven.clontz@gmail.com>
Date: Fri, 25 Apr 2025 12:50:26 -0500
Subject: [PATCH 1/3] clarify how to show computation of inverse

---
 source/linear-algebra/exercises/outcomes/MX/MX2/template.xml | 5 ++---
 1 file changed, 2 insertions(+), 3 deletions(-)

diff --git a/source/linear-algebra/exercises/outcomes/MX/MX2/template.xml b/source/linear-algebra/exercises/outcomes/MX/MX2/template.xml
index a575c7d38..10edc36a7 100644
--- a/source/linear-algebra/exercises/outcomes/MX/MX2/template.xml
+++ b/source/linear-algebra/exercises/outcomes/MX/MX2/template.xml
@@ -62,9 +62,8 @@ be done without using technology.)
             <outtro>
                 <p>
 <!-- {{#invertible}} -->
-Show how to compute each column of the inverse matrix
-by solving an appropriate vector equation (that is, computing RREF
-of an appropriate augmented matrix).
+Show how to solve <m>{{label}} \vec x = \vec e_i</m> for <m>i=1,2,3,4</m> to obtain
+each column <m>{{label}}^{-1}\vec e_i</m> of the inverse matrix <m>{{label}}^{-1}</m>.
 <!-- {{/invertible}} -->
 <!-- {{^invertible}} -->
 N/A

From 2f6e782b2000fc66963f8edc6e7289b092d75eb6 Mon Sep 17 00:00:00 2001
From: Steven Clontz <steven.clontz@gmail.com>
Date: Fri, 25 Apr 2025 12:51:51 -0500
Subject: [PATCH 2/3] Update template.xml

---
 source/linear-algebra/exercises/outcomes/MX/MX2/template.xml | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/source/linear-algebra/exercises/outcomes/MX/MX2/template.xml b/source/linear-algebra/exercises/outcomes/MX/MX2/template.xml
index 10edc36a7..7a7816da5 100644
--- a/source/linear-algebra/exercises/outcomes/MX/MX2/template.xml
+++ b/source/linear-algebra/exercises/outcomes/MX/MX2/template.xml
@@ -25,10 +25,10 @@ discussing its corresponding linear transformation.
                 </p>
                 <p>
 <!-- {{#invertible}} -->
-<m>{{label}}</m> is invertible.
+<m>{{label}}</m> is invertible because it is a bijective transformation.
 <!-- {{/invertible}} -->
 <!-- {{^invertible}} -->
-<m>{{label}}</m> is not invertible.
+<m>{{label}}</m> is not invertible because it is not a bijective transformation.
 <!-- {{/invertible}} -->
                 </p>
             </outtro>

From c8946b5b5eff21379f60d13c58f5a8554051871c Mon Sep 17 00:00:00 2001
From: Steven Clontz <steven.clontz@gmail.com>
Date: Thu, 22 May 2025 15:06:02 -0500
Subject: [PATCH 3/3] Update
 source/linear-algebra/exercises/outcomes/MX/MX2/template.xml

Co-authored-by: jkostiuk <kostiuk.jordan@gmail.com>
---
 source/linear-algebra/exercises/outcomes/MX/MX2/template.xml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/source/linear-algebra/exercises/outcomes/MX/MX2/template.xml b/source/linear-algebra/exercises/outcomes/MX/MX2/template.xml
index 7a7816da5..ad4a899bd 100644
--- a/source/linear-algebra/exercises/outcomes/MX/MX2/template.xml
+++ b/source/linear-algebra/exercises/outcomes/MX/MX2/template.xml
@@ -62,7 +62,7 @@ be done without using technology.)
             <outtro>
                 <p>
 <!-- {{#invertible}} -->
-Show how to solve <m>{{label}} \vec x = \vec e_i</m> for <m>i=1,2,3,4</m> to obtain
+Explain and demonstrate how to solve <m>{{label}} \vec x = \vec e_i</m> for <m>i=1,2,3,4</m> to obtain
 each column <m>{{label}}^{-1}\vec e_i</m> of the inverse matrix <m>{{label}}^{-1}</m>.
 <!-- {{/invertible}} -->
 <!-- {{^invertible}} -->