|
|
| Line 1: |
Line 1: |
| − | <div id=" 16SpaceContent" align="left"><div class="ZEditBox" align="justify"> | + | <div style="font-size:30px">'''MDETERM(arr)'''</div><br/> |
| | + | *where <math>arr</math> is the array of numeric elements |
| | | | |
| − | Syntax
| |
| | | | |
| − | </div></div>
| + | ==Description== |
| − | ---- | + | *This function gives the determinant value of a matrix. |
| − | <div id="4SpaceContent" align="left"><div class="ZEditBox" align="justify">
| + | *To calculate the determinant of the matrix we can choose only square matrix. |
| | + | *i.e., Number rows and number of columns should be equal.Determinant of the identity matrix is always 1. *Determinant of the matrix A is denoted by det(A) or |A|. |
| | + | *Let A be 2x2 matrix with the elements A=[a b |
| | + | c d]. |
| | + | *Then det(A)=ad-bc, where a,b,c,d all are real numbers. |
| | + | *Let A be the 3x3 matrix with the elements A=[a b c |
| | + | d e f |
| | + | g h i]. |
| | + | Then |A|=a|e f -b|d f +c|d e |
| | + | h i| g i| g h| |
| | + | =a(ei-fh) -b(di-fg)+c(dh-eg) |
| | + | *Let A be a square matrix of order n. Write A = (a_ij), |
| | + | *Where aij is the entry on the i number of rows and j number of columns and i=1 to n &j=1 to n. |
| | + | *For any i and j, set Aij (called the cofactors), then the general formula for determinant of the matrix A , |A|=summation (j=1 to n)a_ij A_ij, for any fixed i. |
| | + | Also|A|=summation (i=1 to n)a_ij A_ij, for any fixed j. |
| | + | *This function will give the result as error when |
| | + | 1. Any one of the element in array is empty or contain non-numeric |
| | + | 2. Number of rows is not equal to number of columns |
| | | | |
| − | Remarks
| + | ==Examples== |
| | | | |
| − | </div></div>
| |
| − | ----
| |
| − | <div id="2SpaceContent" align="left"><div class="ZEditBox" align="justify">
| |
| | | | |
| − | Examples
| |
| | | | |
| − | </div></div>
| + | ==See Also== |
| − | ----
| |
| − | <div id="8SpaceContent" align="left"><div class="ZEditBox" align="justify">'''<font face="Times New Roman">''''''''''''<font size="6"> </font>''' '''''''''</font>'''</div></div>
| |
| − | ----
| |
| − | <div id="11SpaceContent" align="left"><div class="ZEditBox mceEditable" align="justify">
| |
| | | | |
| − | <font size="5">Description</font>
| + | ==References== |
| − | | |
| − | </div></div>
| |
| − | ----
| |
| − | <div id="10SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">'''<font face="Times New Roman"> <font size="6">MDETERM</font> </font>'''</div></div>
| |
| − | ----
| |
| − | <div id="3SpaceContent" class="zcontent" align="left"><br /><div id="7Space" class="gamizbox" title="7Space"><div id="7SpaceHeader" class="zheaderstyle" title="Double-click to start and stop editing the header."><center></center></div><div id="7SpaceRollup" title="Double-click to rolldown" align="left"><span><span id="7SpaceRollupContent" align="center"></span></span></div><div id="7SpaceCover"><div id="7SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify"><font size="3" face="Times New Roman"> </font>
| |
| − | | |
| − | '''MDETERM'''('''a''')
| |
| − | | |
| − | Where a is a numeric array, have same number of rows and columns.
| |
| − | | |
| − | </div></div>
| |
| − | ----
| |
| − | <div id="13SpaceContent" class="zcontent" align="left"><br /><br /><div id="1Space" class="gamizbox" title="1Space"><div id="1SpaceHeader" class="zheaderstyle" title="Double-click to start and stop editing the header."><center></center></div><div id="1SpaceRollup" title="Double-click to rolldown" align="left"><span><span id="1SpaceRollupContent" align="center"></span></span></div><div id="1SpaceCover"><div id="1SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify"><font size="3"><font face="Times New Roman">
| |
| − | | |
| − | * a can be given as a cell range, {1,2,3;4,5,6;7,8,9}; or as a name to either of these.
| |
| − | * Matrix determinants are generally used for solving systems of mathematical equations that involve several variables.
| |
| − | | |
| − | </font>
| |
| − | | |
| − | <font face="Times New Roman"> </font>
| |
| − | | |
| − | </font></div></div>
| |
| − | ----
| |
| − | <div id="14SpaceContent" class="zcontent" align="left"><br /><br /><br /><div id="5Space" class="gamizbox" title="5Space"><div id="5SpaceHeader" class="zheaderstyle" title="Double-click to start and stop editing the header."><center></center></div><div id="5SpaceRollup" title="Double-click to rolldown" align="left"><span><span id="5SpaceRollupContent" align="center"></span></span></div><div id="5SpaceCover"><div id="5SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify"><font size="3"><font face="Times New Roman">
| |
| − | | |
| − | MDETERM function gives you the matrix determinant of an array.
| |
| − | | |
| − | </font></font></div></div>
| |
| − | ----
| |
| − | <div id="12SpaceContent" class="zcontent" align="left"><br /><br /><br /><div id="9Space" class="gamizbox" title="9Space"><div id="9SpaceHeader" class="zheaderstyle" title="Double-click to start and stop editing the header."><center></center></div><div id="9SpaceRollup" title="Double-click to rolldown" align="left"><span><span id="9SpaceRollupContent" align="center"></span></span></div><div id="9SpaceCover"><div id="9SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">
| |
| − | | |
| − | <font size="3"><font face="Times New Roman"> C1 C2 C3 C4</font></font>
| |
| − | | |
| − | <font size="3"><font face="Times New Roman"></font></font>
| |
| − | | |
| − | <font size="3"><font face="Times New Roman">R1 2 3 4 5</font></font>
| |
| − | | |
| − | <font size="3"><font face="Times New Roman"></font></font>
| |
| − | | |
| − | <font size="3"><font face="Times New Roman">R2 2 5 1 4</font></font>
| |
| − | | |
| − | <font size="3"><font face="Times New Roman"></font></font>
| |
| − | | |
| − | <font size="3"><font face="Times New Roman">R3 5 5 4 6</font></font>
| |
| − | | |
| − | <font size="3"><font face="Times New Roman"></font></font>
| |
| − | | |
| − | <font size="3"><font face="Times New Roman">R4 4 1 5 2</font></font>
| |
| − | | |
| − | <font size="3"><font face="Times New Roman"></font></font>
| |
| − | | |
| − | <font size="3"><font face="Times New Roman"></font></font>
| |
| − | | |
| − | <font size="3"><font face="Times New Roman">That is MDETERM (B2:E5) is 84</font></font>
| |
| − | | |
| − | <font size="3"><font face="Times New Roman"> </font></font>
| |
| − | | |
| − | </div></div>
| |
| − | ----
| |
| − | <div id="6SpaceContent" class="zcontent" align="left">
| |
| − | | |
| − | {| id="TABLE3" class="SpreadSheet blue"
| |
| − | |- class="even"
| |
| − | | class=" " |
| |
| − | <div id="6Space_Copy" title="Click and Drag over to AutoFill other cells."></div>
| |
| − | | Column1
| |
| − | | class=" " | Column2
| |
| − | | class=" " | Column3
| |
| − | | class=" " | Column4
| |
| − | |- class="odd"
| |
| − | | class=" " | Row1
| |
| − | | class="sshl_f" | 2
| |
| − | | class="sshl_f" | 3
| |
| − | | class="sshl_f" | 4
| |
| − | | class="sshl_f" | 5
| |
| − | |- class="even"
| |
| − | | class=" " | Row2
| |
| − | | class="sshl_f " | 2
| |
| − | | class="sshl_f" | 5
| |
| − | | class="sshl_f" | 1
| |
| − | | class="sshl_f" | 4
| |
| − | |- class="odd"
| |
| − | | Row3
| |
| − | | class="sshl_f" | 5
| |
| − | | class="sshl_f" | 5
| |
| − | | class="sshl_f" | 4
| |
| − | | class="sshl_f" | 6
| |
| − | |- class="even"
| |
| − | | Row4
| |
| − | | class="sshl_f" | 4
| |
| − | | class="sshl_f" | 1
| |
| − | | class="sshl_f" | 5
| |
| − | | class="sshl_f " |
| |
| − | <div id="6Space_Handle" title="Click and Drag to resize CALCI Column/Row/Cell. It is EZ!"></div><div id="6Space_Copy" title="Click and Drag over to AutoFill other cells."></div>2
| |
| − | |- class="odd"
| |
| − | | class=" " | Row5
| |
| − | | class="sshl_f" | 84
| |
| − | | class="sshl_f" |
| |
| − | | class="sshl_f" |
| |
| − | | class="sshl_f" |
| |
| − | |- class="even"
| |
| − | | Row6
| |
| − | | class="sshl_f SelectTD SelectTD" |
| |
| − | <div id="6Space_Handle" title="Click and Drag to resize CALCI Column/Row/Cell. It is EZ!"></div><div id="6Space_Copy" title="Click and Drag over to AutoFill other cells."></div>
| |
| − | | class="sshl_f" |
| |
| − | | class="sshl_f" |
| |
| − | | class="sshl_f" |
| |
| − | |}
| |
| − | | |
| − | <div align="left">[[Image:calci1.gif]]</div></div>
| |
| − | ----
| |
| − | </div></div></div></div></div></div></div></div></div></div></div></div>
| |
is the array of numeric elements