Manuals/calci/MDETERM

MDETERM(arr)

• $arr$ is the array of numeric elements

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

Examples

1. =MDETERM({6,4,8;3,6,1;2,4,5}) = 104
2. =DETERM({-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