Pronunciation: /ˈkreɪmərz rul/ Explain
Cramer's rule is an
for solving square
determinants of matrices.
Cramer's rule can only be used with linear systems that have
Cramer's rule is named after
Gabriel Cramer (1704–52),
a Swiss mathematician.
Cramer's rule uses determinants to find the solution of a linear system. For example,
start with the linear system
Now convert this linear system into a 3x4 matrix.
We will be making four determinants out of this matrix. Each of these determinants will
be based on a 3x3 square matrix. The first determinant, which we will label
, is the first three columns of the matrix.
Now find the value of |A0|
The second determinant will be based on the first. Substitute the last column
of matrix A
into the first column of determinant |A0|
new determinant is labeled |Ax|
Now find the value of |Ax|
Continue by finding the determinate of |Ay|
. Do this by
substituting the last column of matrix A
into the second column of
Now repeat the pattern for |Az|
The solution for the linear system is
- McAdams, David E.. All Math Words Dictionary, Cramer's rule. 2nd Classroom edition 20150108-4799968. pg 50. Life is a Story Problem LLC. January 8, 2015. Buy the book
- Skinner, Ernest Brown. College Algebra. pp 92-93. www.archive.org. The Macmillan Company. 1917. Last Accessed 6/25/2018. http://www.archive.org/stream/cu31924031226503#page/n103/mode/1up/search/cramer. Buy the book
- Householder, Alston S.. Principles Of Numerical Analysis. pp 28-29. www.archive.org. McGraw-Hill Book Company, Inc.. 1953. Last Accessed 6/25/2018. http://www.archive.org/stream/principlesofnume030218mbp#page/n47/mode/1up/search/cramer. Buy the book
- McAdams, David E.. Determinant. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 6/27/2018. http://www.allmathwords.org/en/d/determinant.html.
Cite this article as:
McAdams, David E. Cramer's Rule. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/cramersrule.html.
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
6/25/2018: Removed broken links, updated license, implemented new markup, updated GeoGebra apps. (McAdams, David E.)
1/22/2010: Added "References". (McAdams, David E.)
12/27/2008: Corrected url in citation. (McAdams, David E.)
7/1/2008: Initial version. (McAdams, David E.)