The Excel MDETERM Function
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Basic Description
The Excel MDETERM function calculates the determinant of a square matrix.
The format of the function is :
MDETERM( array )
where the array argument is an array of numerical values, that represent a square matrix (i.e. has the
same number of rows as columns).
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Determinant of a Matrix
The Determinant of a square
matrix is a measure of scale.
For the following 2x2 and 3x3 matrices:
The determinant of the 2x2 matrix, A, is :
det(A) = ad - bc
and the determinant of the 3x3 matrix, B, is:
det(B) = a(ei - fh) + b(fg - di) + c(dh - eg)
Further details of the Matrix Determinant are given on the
Wikipedia Determinant Page
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Examples
In the examples below, the Excel Mdeterm function is used to calculate the determinant of a 2x2 and a 3x3 matrix.
Example 1 - 2x2 Matrix
The spreadsheet on the right shows a simple 2x2 matrix. The determinant of this matrix can be calculated
using the Excel Mdeterm function as follows:
=MDETERM( A1:B2 )
This gives the result -9.
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Example 2 - 3x3 Matrix
The determinant of the simple 3x3 matrix on the right can be calculated using the following Excel Mdeterm function:
=MDETERM( A1:C3 )
This gives the result 40.
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A |
B |
C |
1 |
6 |
4 |
2 |
2 |
3 |
5 |
3 |
3 |
2 |
3 |
4 |
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Further information and examples of the Excel Mdeterm function can be found on the
Microsoft Office website.
Common Error
If you get the #VALUE! error from your Excel Mdeterm function, this is likely to be because either:
- the supplied matrix contains blanks or non-numeric values
or
- the supplied matrix has unequal numbers of rows and columns
