LE1 add sageplot 3d visualizations (#907)

Author: StevenClontz

source/linear-algebra/source/01-LE/01.ptx

@@ -422,7 +422,8 @@ system). Otherwise it is <term>inconsistent</term>.<idx><h>linear system</h><h>i
             <ol>
     <li><em>Consistent with one solution:</em>
           its solution set contains a single vector, e.g.
-          <m>\setList{\left[\begin{array}{c}1\\2\\3\end{array}\right]}</m>
+          <m>\setList{\left[\begin{array}{c}1\\2\\3\end{array}\right]}</m>,
+          <xref ref="figure-intersecting-planes-one"/>
                 </li>
                 <li>
                     <em>Consistent with infinitely-many solutions</em>:
@@ -434,16 +435,54 @@ system). Otherwise it is <term>inconsistent</term>.<idx><h>linear system</h><h>i
             }{
               a\in\IR
             }
-          </m>
+          </m>,
+          <xref ref="figure-intersecting-planes-inf"/>
                 </li>
                 <li><em>Inconsistent</em>:
-          its solution set is the empty set, denoted by either <m>\{\}</m> or <m>\emptyset</m>.
+          its solution set is the empty set, denoted by either <m>\{\}</m> or <m>\emptyset</m>, e.g.
+          <xref ref="figure-intersecting-planes-zero"/>
                 </li>
             </ol>
             </p>
         </statement>
     </fact>
 
+    <figure xml:id="figure-intersecting-planes-one">
+        <caption>Intersection of three planes at one point</caption>
+        <image xml:id="LE1-image-intersection-planes-one">
+            <sageplot variant="3d" aspect="1.0">
+<xi:include href="./sage/LE1-image-intersection-planes-one.sage" parse="text"/>
+            </sageplot>
+            <description>
+                <p>Three planes are shown to intersect at a single point. An arrow points to the point of intersection at coordinates <m>(1,2,3)</m>.</p>
+            </description>
+        </image>
+    </figure>
+
+    <figure xml:id="figure-intersecting-planes-inf">
+        <caption>Intersection of three planes at a line</caption>
+        <image xml:id="LE1-image-intersection-planes-inf">
+            <sageplot variant="3d" aspect="1.0">
+<xi:include href="./sage/LE1-image-intersection-planes-inf.sage" parse="text"/>
+            </sageplot>
+            <description>
+                <p>Three planes are shown to intersect along a line of points.</p>
+            </description>
+        </image>
+    </figure>
+
+    <figure xml:id="figure-intersecting-planes-zero">
+        <caption>Three non-mutually-intersecting planes</caption>
+        <image xml:id="LE1-image-intersection-planes-zero">
+            <sageplot variant="3d" aspect="1.0">
+<xi:include href="./sage/LE1-image-intersection-planes-zero.sage" parse="text"/>
+            </sageplot>
+            <description>
+                <p>Three planes are shown to intersect at no common point, although each pair of planes intersects along a line of points.</p>
+            </description>
+        </image>
+    </figure>
+
     <activity estimated-time="10">
         <statement>
             <p>

source/linear-algebra/source/01-LE/sage/LE1-image-intersection-planes-inf.sage

@@ -0,0 +1,9 @@
+x,y,z = var("x y z")
+GREEN = "#90EE90"
+BLUE = "#7070FF"
+PURPLE = "#EE90EE"
+RED = "#FF0000"
+p = implicit_plot3d(x+y+3*z==3,(x,-5,5),(y,-5,5),(z,-5,5),color=GREEN)
+p += implicit_plot3d(2*x-y-3*z==0,(x,-5,5),(y,-5,5),(z,-5,5),color=BLUE)
+p += implicit_plot3d(x==1,(x,-5,5),(y,-5,5),(z,-5,5),color=PURPLE)
+p

source/linear-algebra/source/01-LE/sage/LE1-image-intersection-planes-one.sage

@@ -0,0 +1,10 @@
+x,y,z = var("x y z")
+GREEN = "#90EE90"
+BLUE = "#7070FF"
+PURPLE = "#EE90EE"
+RED = "#FF0000"
+p = implicit_plot3d(-2*x+y+3*z==9,(x,-5,5),(y,-5,5),(z,-5,5),color=GREEN)
+p += implicit_plot3d(x+2*z==7,(x,-5,5),(y,-5,5),(z,-5,5),color=BLUE)
+p += implicit_plot3d(x+y+z==6,(x,-5,5),(y,-5,5),(z,-5,5),color=PURPLE)
+p += arrow3d((0,0,0), (1,2,3), 1,color=RED,thickness=10)
+p

source/linear-algebra/source/01-LE/sage/LE1-image-intersection-planes-zero.sage

@@ -0,0 +1,9 @@
+x,y,z = var("x y z")
+GREEN = "#90EE90"
+BLUE = "#7070FF"
+PURPLE = "#EE90EE"
+RED = "#FF0000"
+p = implicit_plot3d(x+y+3*z==3,(x,-5,5),(y,-5,5),(z,-5,5),color=GREEN)
+p += implicit_plot3d(2*x-y-3*z==0,(x,-5,5),(y,-5,5),(z,-5,5),color=BLUE)
+p += implicit_plot3d(x==3,(x,-5,5),(y,-5,5),(z,-5,5),color=PURPLE)
+p