(*^

::[	frontEndVersion = "Macintosh Mathematica Notebook Front End Version 2.1";
	macintoshStandardFontEncoding; 
	paletteColors = 128; automaticGrouping; currentKernel; 
	fontset = title, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e8,  24, "Times"; ;
	fontset = subtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e6,  18, "Times"; ;
	fontset = subsubtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, italic, e6,  14, "Times"; ;
	fontset = section, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, grayBox, M22, bold, a20,  18, "Times"; ;
	fontset = subsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, blackBox, M19, bold, a15,  14, "Times"; ;
	fontset = subsubsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, whiteBox, M18, bold, a12,  12, "Times"; ;
	fontset = text, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; ;
	fontset = smalltext, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  10, "Times"; ;
	fontset = input, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeInput, M42, N23, bold, L-5,  12, "Courier"; ;
	fontset = output, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5,  12, "Courier"; ;
	fontset = message, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, R65535, L-5,  12, "Courier"; ;
	fontset = print, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5,  12, "Courier"; ;
	fontset = info, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, B65535, L-5,  12, "Courier"; ;
	fontset = postscript, PostScript, formatAsPostScript, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeGraphics, M7, l34, w282, h287,  12, "Courier"; ;
	fontset = name, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, italic,  10, "Geneva"; ;
	fontset = header, inactive, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; ;
	fontset = leftheader, inactive, L2,  12, "Times"; ;
	fontset = footer, inactive, noKeepOnOnePage, preserveAspect, center, M7,  12, "Times"; ;
	fontset = leftfooter, inactive, L2,  12, "Times"; ;
	fontset = help, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  10, "Times"; ;
	fontset = clipboard, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; ;
	fontset = completions, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; ;
	fontset = special1, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; ;
	fontset = special2, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; ;
	fontset = special3, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; ;
	fontset = special4, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; ;
	fontset = special5, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; ;
]
:[font = special1; inactive; preserveAspect; ]
               Vector Spaces, I -- Life in Two and Three Dimensions

Vectors are denoted in Mathematica using curly brackets with commas separting the entries as shown in the cell below.  Evaluate that cell now.
;[s]
6:0,1;67,0;92,2;103,0;188,3;210,0;212,-1;
4:3,13,9,Times,0,12,0,0,0;1,13,9,Times,1,12,0,0,0;1,13,9,Times,2,12,0,0,0;1,13,9,Times,1,12,65535,0,0;
:[font = input; preserveAspect; ]
{1, 2} + {3, 4}

3 {1, 2}

{1, 2, 3} + {4, 5, 6}

5 {1, -1, 2}
:[font = special1; inactive; preserveAspect; ]
For some of the exercises in this module you will want to graph one or more points (represnted as vectors).  The following cell illustrates how this can be done in Mathematica  using the ListPlot
procedure.  Notice that the points to be shown on the graph are specified in a list -- enclosed by curly brackets bwith the vectors separated by commas.  Evaluate the next cell now.  
;[s]
7:0,0;164,1;175,0;187,2;195,0;350,3;376,0;380,-1;
4:4,13,9,Times,0,12,0,0,0;1,13,9,Times,2,12,0,0,0;1,13,9,Times,1,12,0,0,0;1,13,9,Times,1,12,65535,0,0;
:[font = input; preserveAspect; ]
ListPlot[{{1, 2}, {3, 4}}, 
          PlotRange -> {{-4, 4}, {-4, 4}},
          AspectRatio -> Automatic,
          PlotStyle -> {AbsolutePointSize[5]}]
:[font = special1; inactive; preserveAspect; ]
The ranges used for the x- and y-axes are specified in a line of the form

               PlotRange -> {{xlow, xhigh}, {ylow, yhigh}}

with  xlow  and  xhigh  specifying the low and high end for the x-axis and  ylow  and  yhigh   specifying the low and high end of the y-axis. 
;[s]
11:0,0;90,1;133,0;141,2;145,0;152,2;157,0;211,2;215,0;222,2;227,0;278,-1;
3:6,13,9,Times,0,12,0,0,0;1,13,10,Courier,1,12,0,0,0;4,13,9,Times,1,12,0,0,0;
^*)