Manuals/calci/MDETERM

MDETERM(arr)

• where $arr$ 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

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

• 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 $|A|=a{\begin{vmatrix}e&f\\h&i\end{vmatrix}}-b{\begin{vmatrix}d&f\\g&i\end{vmatrix}}+c{\begin{vmatrix}d&e\\g&h\end{vmatrix}}$

               $=a(ei-fh)-b(di-fg)+c(dh-eg)$

• Let A be a square matrix of order n. Write A = (a_ij),
• Where aij is the entry on the i number of rows and j number of columns and i=1 to n &j=1 to n.
• For any i and j, set Aij (called the cofactors), then the general formula for determinant of the matrix A , |A|=summation (j=1 to n)a_ij A_ij, for any fixed i.

Also|A|=summation (i=1 to 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