Manuals/calci/MATRIXDETERMINANT - Revision history

Devika: /* Related Videos */

2019-04-09T19:14:15Z

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2019-04-09T19:13:53Z

Devika: /* Examples */

2019-04-09T19:12:00Z

Examples

Devika at 21:23, 14 June 2017

2017-06-14T21:23:25Z

Devika: Created page with "
'''MATRIXDETERMINANT (a)'''

* $a$ is any square matrix. ==Description== *This function is calculating the determinant of th..."

2017-06-13T20:18:17Z

Created page with "<div style="font-size:30px">'''MATRIXDETERMINANT (a)'''</div><br/> *<math> a </math> is any square matrix. ==Description== *This function is calculating the determinant of th..."

New page

<div style="font-size:30px">'''MATRIXDETERMINANT (a)'''</div><br/>
*<math> a </math> is any square matrix.

==Description==
*This function is calculating the determinant of the given matrix.
*In <math>MATRIXDETERMINANT(a)</math>, <math>a</math> is any square matrix.
*The determinant of a matrix is a special number that can be calculated from a square matrix.
*The determinant of a matrix 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>.

@@ Line 45: / Line 45: @@
 ==Related Videos==
-{{#ev:youtube|v=H9BWRYJNIv4&t=122s|280|center|Detemenants}}
+{{#ev:youtube|v=H9BWRYJNIv4&t=122s|280|center|Determinants}}
 ==See Also==

@@ Line 45: / Line 45: @@
 ==Related Videos==
-{{#ev:youtube|v=H9BWRYJNIv4&t=122s|280|center|Numbers}}
+{{#ev:youtube|v=H9BWRYJNIv4&t=122s|280|center|Detemenants}}
 ==See Also==

@@ Line 42: / Line 42: @@
 #MATRIXDETERMINANT([[8,-4],[12,5]]) =88
 #MATRIXDETERMINANT([1,2,3,4;5,6,-7,8;12,10,-13,15;11,7,5,3]) = 1514
 ==See Also==

← Older revision		Revision as of 21:23, 14 June 2017
Line 37:		Line 37:
	<math>\|A\|=\sum_{j=1}^n a_{ij} A_{ij}</math>, for any fixed <math>i</math>.		<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>.		Also<math>\|A\|=\sum_{i=1}^n a_{ij} A_{ij}</math>, for any fixed <math>j</math>.
		+
		+	==Examples==
		+	#MATRIXDETERMINANT([[6,4,8],[3,6,1],[2,4,5]]) = 104.00000000000001
		+	#MATRIXDETERMINANT([[8,-4],[12,5]]) =88
		+	#MATRIXDETERMINANT([1,2,3,4;5,6,-7,8;12,10,-13,15;11,7,5,3]) = 1514
		+
		+	==See Also==
		+	*[[Manuals/calci/MINVERSE \| MINVERSE ]]
		+	*[[Manuals/calci/MMULT \| MMULT ]]
		+
		+	==References==
		+	*[http://en.wikipedia.org/wiki/Determinant Determinant ]
		+
		+	*[[Z_API_Functions \| List of Main Z Functions]]
		+	*[[ Z3 \| Z3 home ]]

Manuals/calci/MATRIXDETERMINANT - Revision history

Devika: /* Related Videos */

Devika: /* Related Videos */

Devika: /* Examples */

Devika at 21:23, 14 June 2017

Devika: Created page with "'''MATRIXDETERMINANT (a)''' * a is any square matrix. ==Description== *This function is calculating the determinant of th..."

Devika: Created page with "
'''MATRIXDETERMINANT (a)'''

* $a$ is any square matrix. ==Description== *This function is calculating the determinant of th..."