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--- lecture_2_slides_static [2016/01/25 10:31] – rupert
+++ lecture_2_slides_static [2016/01/25 10:34] (current) – rupert
@@ Line 12: / Line 12: @@
 ==== ====
-  * $x+y=1$ This may be viewed as a linear equation in 3 variables, since it is equivalent to $x+y+0z=1$. <html><iframe scrolling="no" src="https://tube.geogebra.org/material/iframe/id/529043/width/800/height/503/border/888888/rc/true/ai/false/sdz/true/smb/false/stb/true/stbh/true/ld/false/sri/true/at/auto" width="800px" height="503px" style="border:0px;"> </iframe></html>
+  * $x+y=1$ This may be viewed as a linear equation in 3 variables, since it is equivalent to $x+y+0z=1$.
+  * {{::xy1.png?nolink&600|}}
 ==== ====
-  * $z=1$, viewed as the equation $0x+0y+z=1$ <html><iframe scrolling="no" src="https://tube.geogebra.org/material/iframe/id/529069/width/800/height/503/border/888888/rc/true/ai/false/sdz/true/smb/false/stb/true/stbh/true/ld/false/sri/true/at/auto" width="800px" height="503px" style="border:0px;"> </iframe><br /></html>This plane is horizontal (parallel to the $x$-$y$ plane).
+  * $z=1$, viewed as the equation $0x+0y+z=1$
+  * {{::z1.png?nolink&600|}}
 ==== Linear equations (in general) ====
@@ Line 38: / Line 40: @@
 $ x+3y+z=5$ and $ 2x+7y+4z=17$.
-  * <html><iframe scrolling="no" src="https://tube.geogebra.org/material/iframe/id/529147/width/800/height/503/border/888888/rc/true/ai/false/sdz/true/smb/false/stb/true/stbh/true/ld/false/sri/true/at/auto" width="800px" height="503px" style="border:0px;"> </iframe></html>
+  * {{::intersection.png?nolink&600|}}
 ==== Intersection of $ x+3y+z=5$ and $ 2x+7y+4z=17$ ====
@@ Line 45: / Line 47: @@
   * Eliminating variables, we get $x=-16+5z$, $y=7-2z$
   * The line of intersection consists of the points $(-16+5z,7-2z,z)$, where $z\in\mathbb{R}$