How to use the MDETERM Function in Excel

In this article, we will learn about how to use the MDETERM function in Excel.

Determinant of a square matrix is a number useful in calculating system of linear equation or calculating the inverse of a matrix.

A Square matrix is matrix which have equal number of rows and columns. Below here are some examples of square matrices.
006
First is a square matrix of 1 x 1. Second is square matrix of 2 x 2. Third matrix is of 3 x 3.

Determinant of a matrix is calculated using the below shown formula.
007
There’s another example shown below for understanding
008
| A | = 3 * 6 - 4 * 8
| A | = - 14
The MDETERM function returns a number representing the determinant of the given input matrix.
Syntax:

=MDETERM(array)

Array : numbers given as cell reference or directly using brackets and semi - colons.
009
The determinant of the above shown matrix is -14.
Let’s understand this function using it in an example.

Here we have 1 x 1 matrix. We need to calculate the determinant of the below shown 1 x 1 matrix.
0010
Use the formula:

=MDETERM (A1)

A2 : array of a number.
0011
Determinant of the number 2 comes out to be 2. So the determinant of 1 x 1 having one number is the number itself.
Now we will calculate the determinant of the 2 x 2 unit matrix shown below.

A unit or identity matrix is whose all diagonal numbers are 1 and all other numbers are zero.
0012
Determinant of a unit matrix is the unit value 1.

array to the MDETERM function is provided as cell reference.

Now we will calculate the determinant of the 3 x 3 matrix shown below.
0013
Use the formula:

=MDETERM(C1:E3)

0014
As you can see here the MDETERM representation of the numbers from the numbers.

All the above example shown are used via giving argument to the function as cell reference.

you could get the determinant of the matrix providing the array directly to the function

Use the formula:

=MDETERM ( { 3, 4; 2, 3 } )

Values along the columns are separated by commas and values in different rows are separated by semi - colons.
0015
Press Enter to view the result.
0016
The determinant of the matrix is 1. But it doesn’t mean this is a unit or identity matrix.

Notes:

  1. The function returns the #VALUE! error if there is any non - numeric value given as argument to the function.
  2. The matrix must be a square matrix i.e. number of rows equal to the number of columns of the matrix or otherwise the function returns the #VALUE! error.

Hope you understood how to use MDETERM function and referring cell in Excel. Explore more articles on Excel mathematical conversion functions here. Please feel free to state your query or feedback for the above article.

 

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Users are saying about us...

  1. REZA HASHEMIAN

    I need to calculate the determinant of a matrix that is constructed from n arbitrary rows and n arbitrary columns of a bigger matrix. How can I do this with Excel? Thanks.

    • You can do this using semicolon and curly braces. For example if you want to get the determinant of rows A1:B5 and columns D5:E9 then use this type of formula =MDETERM({A1:B5;D5:E9})

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