(*^ ::[ Information = "This is a Mathematica Notebook file. It contains ASCII text, and can be transferred by email, ftp, or other text-file transfer utility. It should be read or edited using a copy of Mathematica or MathReader. If you received this as email, use your mail application or copy/paste to save everything from the line containing (*^ down to the line containing ^*) into a plain text file. On some systems you may have to give the file a name ending with ".ma" to allow Mathematica to recognize it as a Notebook. The line below identifies what version of Mathematica created this file, but it can be opened using any other version as well."; FrontEndVersion = "X Window System Mathematica Notebook Front End Version 2.2"; X11StandardFontEncoding; fontset = title, inactive, noPageBreakBelow, noPageBreakInGroup, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e8, 24, fontName, "times"; fontset = subtitle, inactive, noPageBreakBelow, noPageBreakInGroup, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e6, 18, fontName, "times"; fontset = subsubtitle, inactive, noPageBreakBelow, noPageBreakInGroup, nohscroll, preserveAspect, groupLikeTitle, center, M7, italic, e6, 14, fontName, "times"; fontset = section, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, grayBox, M22, bold, a20, 18, fontName, "times"; fontset = subsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, blackBox, M19, bold, a15, 14, fontName, "times"; fontset = subsubsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, whiteBox, M18, bold, a12, 12, fontName, "times"; fontset = text, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, fontName, "times"; fontset = smalltext, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 10, fontName, "times"; fontset = input, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeInput, M42, N23, bold, 12, fontName, "courier"; fontset = output, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5, 12, fontName, "courier"; fontset = message, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, 12, fontName, "courier"; fontset = print, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, 12, fontName, "courier"; fontset = info, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, 12, fontName, "courier"; fontset = postscript, PostScript, formatAsPostScript, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeGraphics, M7, l34, w282, h287, 12, fontName, "courier"; fontset = name, inactive, noPageBreakInGroup, nohscroll, preserveAspect, M7, italic, B65535, 10, fontName, "times"; fontset = header, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, italic, 12, fontName, "times"; fontset = leftheader, 12, fontName, "times"; fontset = footer, inactive, nohscroll, noKeepOnOnePage, preserveAspect, center, M7, italic, 12, fontName, "times"; fontset = leftfooter, 12, fontName, "times"; fontset = help, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, fontName, "times"; fontset = clipboard, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, fontName, "times"; fontset = completions, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, fontName, "courier"; fontset = special1, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, fontName, "times"; fontset = special2, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, fontName, "times"; fontset = special3, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, fontName, "times"; fontset = special4, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, fontName, "times"; fontset = special5, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, fontName, "times";paletteColors = 128; automaticGrouping; currentKernel; ] :[font = title; inactive; preserveAspect; startGroup] Computer HW #1 due 9/16 :[font = input; preserveAspect] Your Name Here. ;[s] 2:0,0;15,1;16,-1; 2:1,0,0 ,times,1,18,0,0,0;1,0,0 ,courier,1,12,0,0,0; :[font = input; preserveAspect] Due 9/16. Worth 5 extra credit points. :[font = input; preserveAspect] There are 5 systems of linear equations. For each one, find the matricies Mand b such that Mx= b is the system (where x is an column of the appropriate variables), show this is the case, find the augmented matrix AugA of the system, write AugA in reduced row-echelon form, find all solutions of the system, and if possible, compute M^2 and the inverse of M. Print out your solutions. ;[s] 19:0,0;75,1;76,2;81,3;82,4;95,5;98,6;99,7;100,8;122,9;123,10;225,11;229,12;252,13;256,14;347,15;351,16;371,17;372,18;400,-1; 19:1,0,0 ,times,0,12,0,0,0;1,0,0 ,times,1,12,0,0,0;1,0,0 ,times,0,12,0,0,0;1,0,0 ,times,1,12,0,0,0;1,0,0 ,times,0,12,0,0,0;1,0,0 ,times,1,12,0,0,0;1,0,0 ,times,0,12,0,0,0;1,0,0 ,times,1,12,0,0,0;1,0,0 ,times,0,12,0,0,0;1,0,0 ,times,1,12,0,0,0;1,0,0 ,times,0,12,0,0,0;1,0,0 ,times,1,12,0,0,0;1,0,0 ,times,0,12,0,0,0;1,0,0 ,times,1,12,0,0,0;1,0,0 ,times,0,12,0,0,0;1,0,0 ,times,1,12,0,0,0;1,0,0 ,times,0,12,0,0,0;1,0,0 ,times,1,12,0,0,0;1,0,0 ,times,0,12,0,0,0; :[font = input; preserveAspect] 1.) 5 x1 + 5 x2 + 2 x3 + 3 x4 + 7 x5 - x6 = 1 6 x1 + 2 x2 + 7 x3 + 7 x4 + 3 x5 + x6 = 17 9 x 1 + 8 x2 + 10 x3 + 6 x4 + 4 x5 - 3x6 = 2 8 x1 + 4 x2 + 2 x3 + 5 x4 + x5 = 4 3 x 1 + 10 x2 + 2 x3 + 7 x4 + x5 + 7x6 = 10 ;[s] 1:0,0;435,-1; 1:1,0,0 ,times,0,14,0,0,0; :[font = input; preserveAspect] 2.) 5 x1 + 5x2 + 2 x3 + 3 x4 = 0 6 x1 + 2x2 + 7 x3 + 7 x4 = 0 9 x 1 + 8 x2 + 10 x3 + 6 x4 = 0 ;[s] 2:0,0;11,1;170,-1; 2:1,0,0 ,courier,0,12,0,0,0;1,0,0 ,times,0,14,0,0,0; :[font = input; preserveAspect] 3.) x1 + 2x2 - 3x3 + 4x4 = -5 6x1 - 7x2 + 8x3 + 9x4 = 10 11x1 - 12x2 12x4 = 3 3x1 - x2 + 17x3 = -9 ;[s] 1:0,0;175,-1; 1:1,0,0 ,courier,0,12,0,0,0; :[font = input; preserveAspect] 4.) x1 + 2x2 - 3x3 + 4x4 = 0 6x1 - 7x2 + 8x3 + 9x4 = 0 11x1 - 12x2 12x4 = 0 3x1 - x2 + 17x3 = 0 ;[s] 1:0,0;171,-1; 1:1,0,0 ,courier,0,12,0,0,0; :[font = input; preserveAspect; endGroup] 5.) x1 + 2x2 - 3x3 + 4x4 = -5 6x1 - 7x2 + 8x3 + 9x4 = 10 11x1 - 12x2 12x4 = 3 4x1 - 7x2 - 5x_3 - x4 = -3 ;[s] 4:0,0;1,1;8,2;10,3;177,-1; 4:1,0,0 ,courier,1,12,0,0,0;1,0,0 ,times,0,12,0,0,0;1,0,0 ,courier,1,12,0,0,0;1,0,0 ,courier,0,12,0,0,0; ^*)