Manuals/calci/MDETERM

MDETERM(a)

• $a$ is the array of numeric elements.
  • MDETERM(), returns the matrix determinant of an array.

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 $A$ is denoted by $det(A)$ or $|A|$.
• Let $A$ be 2x2 matrix with the elements

$A={\begin{bmatrix}a&b\\c&d\\\end{bmatrix}}$

• Then $det(A)=ad-bc$, where $a,b,c,d$ all are real numbers.
• Let $A$ be the 3x3 matrix with the elements

$A={\begin{bmatrix}a&b&c\\d&e&f\\g&h&i\\\end{bmatrix}}$ Then $|A|=a{\begin{vmatrix}e&f\\h&i\end{vmatrix}}-b{\begin{vmatrix}d&f\\g&i\end{vmatrix}}+c{\begin{vmatrix}d&e\\g&h\end{vmatrix}}$: $|A|=a(ei-fh)-b(di-fg)+c(dh-eg)$

• Let $A$ be a square matrix of order $n$. Write $A=(a_{ij})$,
• Where $a_{ij}$ is the entry on the $i^{th}$ row and $j^{th}$ column and $i=1$ to $n$ & $j=1$ to $n$.
• For any $i$ and $j$, 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 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} is,

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

ZOS

• The syntax is to calculate determinant of a matrix in ZOS is 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 MDETERM(a)} .
  • 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} is the array of numeric elements.
• For e.g.,MDETERM([[2.3,4.1,5.9],[3.5,6.2,1.3],[2.8,9.1,8.4]])

Examples

1. =MDETERM([[6,4,8],[3,6,1],[2,4,5]]) = 104
2. =MDETERM([[-5,10],[6,-8]]) = -20
3. =MDETERM([[1,0,2,1],[4,0,2,-1],[1,4,5,2],[3,1,2,0]]) = 17
4. =MDETERM([1,2,3],[5,2,8]) = NAN

Related Videos

Determinant of Matrix

See Also

• MINVERSE
• MMULT

References

Determinant

• List of Main Z Functions

• Z3 home