Rule of Sarrus
Encyclopedia
Determinant
In linear algebra, the determinant is a value associated with a square matrix. It can be computed from the entries of the matrix by a specific arithmetic expression, while other ways to determine its value exist as well...
of a 3×3 matrix
Matrix (mathematics)
In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries. An example of a matrix with six elements isMatrices of the same size can be added or subtracted element by element...
. It is named after the French mathematician Pierre Frédéric Sarrus
Pierre Frédéric Sarrus
Pierre Frédéric Sarrus was a French mathematician.Sarrus was professor at the University of Strasbourg, France and member of the French Academy of Sciences in Paris ....
.
Consider a 3×3 matrix
then its determinant can be computed by the following scheme:
Write out the first 2 columns of the matrix to the right of the 3rd column, so that you have 5 columns in a row. Then add the products of the diagonals going from top to bottom (solid) and subtract the products of the diagonals going from bottom to top (dashed). This yields:
A similar scheme based on diagonals works for 2x2 matrices:
Both are special cases of the Leibniz formula, which however does not yield similar memorization schemes for larger matrices. Sarrus' rule can also be derived by looking at the Laplace expansion
Laplace expansion
In linear algebra, the Laplace expansion, named after Pierre-Simon Laplace, also called cofactor expansion, is an expression for the determinant |B| of...
of a 3×3 matrix.
External links
- Sarrus' rule at Planetmath
- Linear Algebra: Rule of Sarrus of Determinants at khanacademy.org