MX2 Fixes

source/linear-algebra/exercises/outcomes/MX/MX2/generator.sage

@@ -14,7 +14,7 @@ class Generator(BaseGenerator):
         constants = A*solution
         m = A.augment(constants, subdivide=True)
         ordinal = randrange(1,4)
-        ordinal_string = ["1st", "2nd", "3rd", "4th"][ordinal]
+        ordinal_string = ["first", "second", "third", "fourth"][ordinal]
         ord_matrix = A.augment(column_matrix(
             identity_matrix(4).column(ordinal)),
             subdivide=True)
@@ -43,6 +43,7 @@ class Generator(BaseGenerator):
             "invertible": False,
             "label": labels[1],
             "vector_eq": TBIL.VectorEquation(m),
+            "ordinal": ordinal_string,
         }]
 
         shuffle(matrices)

source/linear-algebra/exercises/outcomes/MX/MX2/template.xml

@@ -25,24 +25,30 @@ discussing its corresponding linear transformation.
                 </p>
                 <p>
 <!-- {{#invertible}} -->
-<m>{{label}}</m> is invertible.
+<m>{{label}}</m> is invertible because its transformation is bijective.
 <!-- {{/invertible}} -->
 <!-- {{^invertible}} -->
-<m>{{label}}</m> is not invertible.
+<m>{{label}}</m> is not invertible because its transformation is not bijective.
 <!-- {{/invertible}} -->
                 </p>
             </outtro>
         </knowl>
         <knowl>
             <content>
                 <p>
-If the matrix is invertible, use technology to find its inverse.
+If the matrix is invertible, explain and demonstrate how to find the
+{{ordinal}} column of this inverse by solving an appropriate linear system
+or vector equation.
                 </p>
             </content>
             <outtro>
                 <p>
 <!-- {{#invertible}} -->
-Its inverse is <m>{{inverse}}</m>.
+Since
+<me>
+\operatorname{RREF} {{ord_matrix}} = {{ord_rref}}
+</me>
+the {{ordinal}} column of the inverse is <m>{{ord_col}}</m>.
 <!-- {{/invertible}} -->
 <!-- {{^invertible}} -->
 N/A
@@ -53,20 +59,13 @@ N/A
         <knowl>
             <content>
                 <p>
-If the matrix is invertible, explain and demonstrate how to find the
-{{ordinal}} column of this inverse using a technique that could be
-performed without technology (though you may use technology for this
-exercise).
+If the matrix is invertible, use technology to find its inverse.
                 </p>
             </content>
             <outtro>
                 <p>
 <!-- {{#invertible}} -->
-Since
-<me>
-\operatorname{RREF} {{ord_matrix}} = {{ord_rref}}
-</me>
-the {{ordinal}} column of the inverse is <m>{{ord_col}}</m>.
+Its inverse is <m>{{inverse}}</m>.
 <!-- {{/invertible}} -->
 <!-- {{^invertible}} -->
 N/A