Difference between revisions of "Manuals/calci/MDETERM"
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*Where <math>a_{ij}</math> is the entry on the <math>i</math> number of rows and <math>j</math> number of columns and <math>i=1</math> to <math>n</math> & <math>j=1</math> to <math>n</math>. | *Where <math>a_{ij}</math> is the entry on the <math>i</math> number of rows and <math>j</math> number of columns 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 A , | *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 A , | ||
| − | <math>|A|=\sum_{j=1}^n} | + | <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}, for any fixed <math>j</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 | *This function will give the result as error when | ||
1. Any one of the element in array is empty or contain non-numeric | 1. Any one of the element in array is empty or contain non-numeric | ||
Revision as of 05:06, 31 December 2013
- where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle arr} is the array of numeric elements
Description
- This function gives the determinant value of a matrix.
- 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
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A = \begin{bmatrix} a & b \\ c & d \\ \end{bmatrix} }
- Then det(A)=ad-bc, where a,b,c,d all are real numbers.
- Let A be the 3x3 matrix with the elements
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A = \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \\ \end{bmatrix} } Then Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle |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}} : Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle |A| =a(ei-fh) -b(di-fg)+c(dh-eg)}
- Let be a square matrix of order Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n} . Write Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A = (a_{ij})} ,
- Where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a_{ij}} is the entry on the Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle i} number of rows and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle j} number of columns and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle i=1} to Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n} & Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle j=1} to Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n} .
- For any Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle i} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle j} , set Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A_{ij}} (called the co-factors), then the general formula for determinant of the matrix A ,
be a square matrix of order Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n}
. Write Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A = (a_{ij})}
,Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle |A|=\sum_{j=1}^n a_{ij} A_{ij}} , for any fixed Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle i} . AlsoFailed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle |A|=\sum_{i=1}^n a_{ij} A_{ij}} , for any fixed Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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
Examples
- =MDETERM({6,4,8;3,6,1;2,4,5}) = 104
- =DETERM({-5,10;6,-8}) = -20
- =MDETERM({1,0,2,1;4,0,2,-1;1,4,5,2;3,1,2,0}) = 17
- =MDETERM({1,2,3;5,2,8}) = NAN