Devika at 10:43, 26 May 2020

2020-05-26T10:43:45Z

Devika at 21:23, 14 June 2017

2017-06-14T21:23:20Z

Devika at 21:46, 21 November 2016

2016-11-21T21:46:02Z

Devika: Created page with "==DET=="

2016-11-21T21:42:37Z

Created page with "==DET=="

New page

==DET==

← Older revision		Revision as of 10:43, 26 May 2020
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	#=DET([[1,0,2,1],[4,0,2,-1],[1,4,5,2],[3,1,2,0]]) = 17		#=DET([[1,0,2,1],[4,0,2,-1],[1,4,5,2],[3,1,2,0]]) = 17
	#=DET([1,2,3],[5,2,8]) = NAN		#=DET([1,2,3],[5,2,8]) = NAN
		+
		+
		+	==Related Videos==
		+
		+	{{#ev:youtube\|v=H9BWRYJNIv4\|280\|center\|Determinants}}

← Older revision		Revision as of 21:23, 14 June 2017
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	==References==		==References==
−	[http://en.wikipedia.org/wiki/Determinant Determinant ]	+	*[http://en.wikipedia.org/wiki/Determinant Determinant ]
		+
		+	*[[Z_API_Functions \| List of Main Z Functions]]
		+	*[[ Z3 \| Z3 home ]]

← Older revision		Revision as of 21:46, 21 November 2016
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−	==DET==	+	<div style="font-size:30px">'''DET(array)'''</div><br/>
		+	*<math>array</math> is the set of numbers.
		+
		+	==Description==
		+	*This function gives the determinant value of a matrix.
		+	*To calculate the determinant of a matrix, we can choose only square matrix.i.e. Number of rows and number of columns should be equal.
		+	*Determinant of the identity matrix is always 1.
		+	*Determinant of the matrix <math>A</math> is denoted by <math>det(A)</math> or <math>\|A\|</math>.
		+	*Let <math>A</math> be 2x2 matrix with the elements
		+	<math>A = \begin{bmatrix}
		+	a & b \\
		+	c & d \\
		+	\end{bmatrix}
		+	</math>
		+	*Then <math>det(A)=ad-bc</math>, where <math>a,b,c,d</math> all are real numbers.
		+	*Let <math>A</math> be the 3x3 matrix with the elements
		+	<math>A = \begin{bmatrix}
		+	a & b & c \\
		+	d & e & f \\
		+	g & h & i \\
		+	\end{bmatrix}
		+	</math>
		+	Then <math>\|A\|=a\begin{vmatrix}
		+	e & f \\
		+	h & i
		+	\end{vmatrix} -b\begin{vmatrix}
		+	d & f \\
		+	g & i
		+	\end{vmatrix} +c\begin{vmatrix}
		+	d & e \\
		+	g & h
		+	\end{vmatrix}</math>:
		+	<math>\|A\| =a(ei-fh)-b(di-fg)+c(dh-eg)</math>
		+	*Let <math>A</math> be a square matrix of order <math>n</math>. Write <math>A = (a_{ij})</math>,
		+	*Where <math>a_{ij}</math> is the entry on the <math>i^{th}</math> row and <math>j^{th}</math> column and <math>i=1</math> to <math>n</math> & <math>j=1</math> to <math>n</math>.
		+	*For any <math>i</math> and <math>j</math>, set <math>A_{ij}</math> (called the co-factors), then the general formula for determinant of the matrix <math>A</math> is,
		+	<math>\|A\|=\sum_{j=1}^n a_{ij} A_{ij}</math>, for any fixed <math>i</math>.
		+	Also<math>\|A\|=\sum_{i=1}^n a_{ij} A_{ij}</math>, for any fixed <math>j</math>.
		+	*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
		+
		+
		+	==Examples==
		+	#=DET([[6,4,8],[3,6,1],[2,4,5]]) = 104
		+	#=DET([[-5,10],[6,-8]]) = -20
		+	#=DET([[1,0,2,1],[4,0,2,-1],[1,4,5,2],[3,1,2,0]]) = 17
		+	#=DET([1,2,3],[5,2,8]) = NAN
		+
		+
		+	==See Also==
		+	*[[Manuals/calci/MINVERSE \| MINVERSE ]]
		+	*[[Manuals/calci/MMULT \| MMULT ]]
		+
		+	==References==
		+	[http://en.wikipedia.org/wiki/Determinant Determinant ]

Manuals/calci/DET - Revision history

Devika at 10:43, 26 May 2020

Devika at 21:23, 14 June 2017

Devika at 21:46, 21 November 2016

Devika: Created page with "==DET=="