May 1, 2024
4 minute read
Cramer's Rule is a method for solving systems of linear equations with the same number of equations as variables. It is named after Gabriel Cramer, a Swiss mathematician who first published the rule in 1750.
Cramer's Rule Formula
Cramer's Rule states that the solution to a system of linear equations is given by,
Solution of x = (Determinant of numerator)/Determinant of whole matrix
where the determinant of the numerator is the determinant of the matrix formed by replacing the column of coefficients of the variable being solved for with the column of constants, and the determinant of the whole matrix is the determinant of the matrix of coefficients.
Example
For example, consider the following system of equations:
x + 2y = 5
3x + 4y = 8
Using Cramer's Rule, we can solve for x as follows:
Determinant of numerator =
|5 2|
|8 4| = 20 - 16 = 4
Determinant of whole matrix =
|1 2|
|3 4| = 4 - 6 = -2
So, x = 4/-2 = -2.
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Find a path to becoming a Cramer's Rule. Learn more at:
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Reading list
We've selected five books
that we think will supplement your
learning. Use these to
develop background knowledge, enrich your coursework, and gain a
deeper understanding of the topics covered in
Cramer's Rule.
This classic work by Gabriel Cramer is the original source of Cramer's Rule. It provides a detailed exposition of the rule and its applications in geometry and physics.
Develops a computational approach to Cramer's Rule that makes it more efficient to use in practice. It is suitable for researchers and practitioners who need to solve large systems of linear equations.
This comprehensive textbook covers a wide range of topics in linear algebra, including Cramer's Rule. It valuable resource for students who want to gain a deeper understanding of the subject.
This German-language textbook provides a clear and concise introduction to linear algebra, including Cramer's Rule. It is suitable for students and professionals who want to learn the basics of the subject.
This beginner-friendly book provides a step-by-step guide to using Cramer's Rule. It is ideal for students who are new to the subject or who need a refresher.
For more information about how these books relate to this course, visit:
OpenCourser.com/topic/qq6h1w/cramer
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