A determinant is calculated by multiplying the diagonals of the matrix, then adding or subtracting the products of the diagonals. For the 2x2 matrix
Figure 1 shows how to find the determinant of a 3x3 matrix.. The first diagonals go from top left to bottom right. The numbers multiplied are a11 · a22 · a33, then a12·a23·a31, then a13·a21·a32. The product of these diagonals are added together.
The diagonals from upper right to bottom left are calculated. The numbers multiplied are a13·a22·a31, then a12·a21·a33, then a11·a23·a32. These products are subtracted from the previous sum.
The function for the determinant of a 3x3 matrix is
|A| = a11·a22·a33 +
Figure 1: The determinant of a 3x3 matrix
Cite this article as:
McAdams, David E. Determinant of a Matrix. 4/20/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/d/determinant.html.
Revision History 4/20/2019: Updated equations and expressions to the new format (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
7/4/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
1/23/2010: Added "References". (McAdams, David E.)
1/9/2009: Added Laplace Expansion to 'More Information'. (McAdams, David E.)
12/27/2008: Changed '3xe matrix' to '3x3 matrix'. (McAdams, David E.)
12/3/2008: Initial version. (McAdams, David E.)
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