add GT5 checkit

source/linear-algebra/exercises/bank.xml

@@ -257,6 +257,14 @@
                 with a given eigenvalue.
             </description>
         </outcome>
+        <outcome>
+            <title>Change of Basis</title>
+            <path>outcomes/GT/GT5</path>
+            <slug>GT5</slug>
+            <description>
+                Calculate the change-of-basis matrix between two bases of R^n.
+            </description>
+        </outcome>
         <outcome>
             <title>Multiple Choice Midterm</title>
             <path>outcomes/Extra/Extra1Midterm</path>

source/linear-algebra/exercises/outcomes/GT/GT5/generator.sage

@@ -0,0 +1,28 @@
+load("../../../source/common/sagemath/library.sage")
+TBIL.config_matrix_typesetting()
+
+class Generator(BaseGenerator):
+    def data(self):
+        # create a 3x3 invertible matrix
+        A = CheckIt.simple_random_matrix_of_rank(3,rows=3,columns=3)
+        new_vector = column_matrix(
+            vector(QQ, [randrange(1,5)*choice([-1,1]) for _ in range(3)])
+        )
+        old_vector = A*new_vector
+        lin_combo_exp = TBIL.LinearCombination(
+            [
+                new_vector[i]
+                for i in range(3)
+            ],
+            [
+                column_matrix(A.column(i))
+                for i in range(3)
+            ],
+        )
+        return {
+            "M_B": A^(-1),
+            "v": old_vector,
+            "lin_combo_exp": lin_combo_exp,
+            "vecset": TBIL.VectorSet(A.columns()),
+        }
+

source/linear-algebra/exercises/outcomes/GT/GT5/template.xml

@@ -0,0 +1,34 @@
+<?xml version='1.0' encoding='UTF-8'?>
+<knowl mode="exercise" xmlns="https://spatext.clontz.org" version="0.2">
+    <intro>
+        <p>
+Let <m>\mathcal{B}= {{vecset}}</m>, and <m>\vec{v}= {{v}}</m>.
+        </p>
+    </intro>
+    <knowl>
+        <content>
+            <p>
+Explain and demonstrate how to verify that <m>\mathcal{B}</m> is a basis of <m>\mathbb R^3</m>
+and how to calculate <m>M_\mathcal{B}</m>, the change-of-basis matrix from the standard basis of
+<m>\mathbb R^3</m> to <m>\mathcal{B}</m>.
+            </p>
+        </content>
+        <outtro>
+            <p><m>M_{\mathcal B} = {{M_B}}</m></p>
+        </outtro>
+    </knowl>
+
+    <knowl>
+        <content>
+            <p>
+Explain and demonstrate how to use <m>M_\mathcal{B}</m> to express <m>\vec{v}</m> in terms of
+<m>\mathcal{B}</m>-basis vectors. 
+            </p>
+        </content>
+        <outtro>
+            <p>
+                <m>{{v}} = {{lin_combo_exp}}</m>
+            </p>
+        </outtro>
+    </knowl>
+</knowl>

source/linear-algebra/exercises/outcomes/MX/MX3/generator.sage

@@ -22,5 +22,6 @@ class Generator(BaseGenerator):
             result["system"] = CheckIt.latex_system_from_matrix(m)
         else:
             result["vector_eq"] = TBIL.VectorEquation(m)
+
         return result
 

source/linear-algebra/source/05-GT/outcomes/05.ptx

@@ -0,0 +1,4 @@
+<?xml version='1.0' encoding='UTF-8'?>
+<p>
+Calculate the change-of-basis matrix between two bases of <m>\IR^n</m>.
+</p>

source/linear-algebra/source/05-GT/outcomes/main.ptx

@@ -19,8 +19,8 @@ By the end of this chapter, you should be able to...
         <li>
             <xi:include href="./04.ptx"/>
         </li>
-<!--         <li>
+        <li>
             <xi:include href="./05.ptx"/>
-        </li> -->
+        </li>
     </ol>
 </objectives>