Manuals/calci/MDETERM

MDETERM(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 $A_{ij}$ (called the co-factors), then the general formula for determinant of the matrix $A$ is,

$|A|=\sum _{j=1}^{n}a_{ij}A_{ij}$ , for any fixed $i$ . Also $|A|=\sum _{i=1}^{n}a_{ij}A_{ij}$ , 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

ZOS

The syntax is to calculate determinant of a matrix in ZOS is .
- $a$ 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]])