.MCAD 310000000 \  docDocument MmcObject[  dim_formatTmasslengthtimecharge temperature luminosity substanceNumericalFormatQdii  shpRectVmcDocumentObjectState\ mcPageModelK????mcHeaderFooterI@I |P CHeaderFooterJ@l{\rtf1\ansi\deff0\deflang1033{\fonttbl{\f0\fswiss\fprq15 Arial;}} \viewkind4\uc1\pard\f0\fs18\{d\}\par } @{\rtf1\ansi\deff0\deflang1033{\fonttbl{\f0\fswiss\fprq15\fcharset0 Arial;}{\f1\fswiss\fprq15 Arial;}} \viewkind4\uc1\pard\qc\f0\fs18 Essentials\f1\par } @{\rtf1\ansi\deff0\deflang1033{\fonttbl{\f0\fswiss\fprq15\fcharset0 Arial;}{\f1\fswiss\fprq15 Arial;}} \viewkind4\uc1\pard\qr\f0\fs18 Matrices \{n\}\f1\par } @J@{\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fnil\fprq15 Arial;}{\f3\fswiss Arial;}{\f4\fswiss\fprq15 Arial;}} {\colortbl\red0\green0\blue0;} \deflang1033\pard\plain\f4\fs18 \par } @{\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fnil\fprq15 Arial;}{\f3\fswiss Arial;}{\f4\fswiss\fprq15 Arial;}} {\colortbl\red0\green0\blue0;} \deflang1033\pard\qc\plain\f3\fs20 \par } @{\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fnil\fprq15 Arial;}{\f3\fswiss Arial;}{\f4\fswiss\fprq15 Arial;}} {\colortbl\red0\green0\blue0;} \deflang1033\pard\qr\plain\f4\fs18 \par } @J@J MbP?MbP? TextState? TextStyle>@ ArialSerial_ParPropDefaultWNormal>@Arial@W Heading 1>@ Arial@W Heading 2>@ Arial@W Heading 3 >@ Arial@W Paragraph >@ Arial@WList >@ Arial@WIndent >@Times New Roman@W Title >@Times New Roman@W Subtitle font_style_listO font_styleP  VariablesTimes New Roman@P  ConstantsTimes New Roman@P TextArial@P Greek VariablesSymbol@P User 1Arial@P User 2 Courier New@P User 3Arial@P User 4Times New Roman@P User 5Times New Roman@P User 6Arial@P User 7Times New Roman@P SymbolsSymbol@P Current Selection FontArial@P Undefined Font@P HeaderArial@P FooterArial@P Rotated Math FontTimes New RomanA TextRegion* docRegionGshpBoxURAJJ CharacterMap-RangeMap;Matrices ChrPropMap7 ParPropMap9 RangeElem< ParPropData: RangeData=@WEmbedMap1<LinkMap/<LinkData0@NormalArial *@U+;8Azz-Standard notation: 7< ChrPropData8mArial<89<:@W1</<0@NormalArial *@U+?8  -2Mi,j is the value in row i, column j of matrix M. 72< 8!<"8_#<.$8!#!92%<2&:@W1'</2(<2)0@NormalArial **@UK[XA-Number of elements: 7+<,8*mArial-<.8*+-+9/<0:@W11</2<30@NormalArial 4*@UK5kX}} } -@Mathcad numbers the rows and columns of matrices starting with zero. If i := 0..imax, then there are imax+1 rows in the array. 795<6:@W17</8<90@NormalArial :*@U{3A++-Origin:7;<<8:mArial9=<>:@W1?</@@<@A0@NormalArial @B*@U{&nn n -@|If Origin:=1 is written, then the counting starts at 1 rather than zero. This statement should be used carefully, if at all.7|9|@C<|@D:@W1@E</|@F<|@G0@NormalArial @H*@U8xx-Typing in a matrix:7@I<@J8@HiArial9@K<@L:@W1@M</@N<@O0@NormalArial @P*@U0  -@To create a matrix type the variable name, then open the Matrix toolbar, select the matrix, then the number of rows and columns.79@Q<@R:@W1@S</@T<@U0@NormalArial @V*@Ud  LL- For example,7 9 @W< @X:@W1@Y</ @Z< @[0@NormalArial @\eqRegionB@U @]tree@ p@^@@ @]@_@@d@^M@`@@p@^@a@@0@`@b@@0A@a@c@@0A@b@d@@0A@c@e@@0A@d@f@@0A@e@g@@@@f@h@@@f6@i@@@e4@j@@@d2@k@@@c4@l@@@b3@m@@@a1@n@B@UPb @o@@ p@p@@ @o@q@@d@pN@r@@p@p@s@@0@r@t@@0A@s@u@@0A@t@v@@0A@u@w@@@@v@x@@@v4@y@@@u2@z@@@t3@{@@@s1@|@B@U,D8@}@@ p@~@@@}@@@@@~@@@d@M@@@ @@@@t@0@@@@0@@@@~@@@+@@Serial_DisplayNodeX@@@@@@B@U0,lDU8@@@ p@@@@@@@@@@@@d@M@@@ @@@@t@0@@@@1@@@@@@@+@@@X@@@@@@B@UX4qEc@@@@ p@@@@then@*@U3%S@ -:Note that the 1,1 element is NOT the upper left element. 7:9:@<:@:@W1@</:@<:@0@NormalArial @@B@ULdX@@@ p@@@@@@@@@@@@d@M@@@ @@@@t@1@@@@0@@@@@@@+@@@X@@@@@@B@U0LldUX@@@ p@@@@@@@@@@@@d@M@@@ @@@@t@1@@@@1@@@@@@@+@@@X@@@@@*@U{A-&To find the number of rows or columns:7&@<&@8@mArial9&@<&@:@W1@</&@<&@0@NormalArial @@B@U0|~g@@@ p@@@@@@@@@@@@d@rows@@@p@@@@@M@@@@@@@+@@@X@@@@@@B@U|@@@ p@@@@@@@@@@@@d@cols@@@p@@@@@M@@@@@@@+@@@X@@@@@*@Uskk-The transpose is 7 @< @8@mArial@<@8@@@@9@<@:@W1@</@<@0@NormalArial @@B@U@@@ p@@@@@@@@@@@@d@M@@@@@@@+@@@X@@@@@*@Uh""P P -The reverse: (by rows)7 @<@8@@<@8@mArial@@< @8@@@@9@<@:@W1@</@<@0@NormalArial @@B@U@@@ p@@@@@@@@@@@@d@reverse@@@p@@@@@M@@@@@@@+@@@X@@@@@*@Uo gg-Column selector7@<@8@mArial9@<@:@W1@</@<@0@NormalArial @@B@U#@@@ p@@@@A@@4@@A@@dAMA@@A1A@@@A@@+@A@XA@@AA*@U(.!w w -To create a vector from a row:7A<A8AmArial9A <A :@W1A </A <A 0@NormalArial A@B@U  A@@ pA@@AA@@4@AA@@p@AA@@AA@@dAMA@@A0A@@AA@@+@A@XA@@AA*@Ux3)S@ -:This command does not work for a matrix that is not square7:9:A<:A:@W1A</:A<:A0@NormalArial A*@U;^KHVV- Determinant: 7 A < A!8AmArial9 A"< A#:@W1A$</ A%< A&0@NormalArial A'@B@U<MHA(@@ pA)@@A(A*@@{@A)A+@@A*NA,@@A)A-@@+@A,@XA.@@A,A/@B@U(<^MGHA0@@ pA1@@@A0A2@@A1A3@@{@A2A4@@A3MA5@@A2A6@@+@A5@XA7@@A5A8*@Us !@@-@xVectorized equations in which the operation is performed term by term (select the vectorize operator from the taskbar): 7xA9<A:8A8mArialA;:@W1A?</xA@<2B?0@NormalArial B@@B@Up)BA@@ pBB@@BABC@@@BBBD@@dBC submatrixBE@@pBCBF@@ BEBG@@ @BFBH@@ @BGBI@@ @BHBJ@@dBIMBK@@BI1BL@@BH2BM@@BG0BN@@BF1BO@@BBBP@@+@BO@XBQ@@BOBR@B@UTBS@@ pBT@@BSBU@@dBTMBV@@BTBW@@+@BV@XBX@@BVBY*@UPX -,We have selected rows 1 and 2 and column 0. 7,9,BZ<,B[:@W1B\</,B]<,B^0@NormalArial B_@B@UpB`@@ pBa@@B`Bb@@@BaBc@@dBb submatrixBd@@pBbBe@@ BdBf@@ @BeBg@@ @BfBh@@ @BgBi@@dBhMBj@@Bh1Bk@@Bg2Bl@@Bf0Bm@@Be0Bn@@BaBo@@+@Bn@XBp@@Bn