linear systems as matrices
(2 hours to learn)
Summary
We can represent systems of linear equations in terms of matrices and vectors. This allows us to analyze and solve them using the tools of linear algebra.
Context
This concept has the prerequisites:
- vectors (Linear systems are represented in terms of matrix-vector multiplication.)
Core resources (read/watch one of the following)
-Free-
→ MIT Open Courseware: Linear Algebra (2011)
Videos for an introductory linear algebra course focusing on numerical methods.
-Paid-
→ Introduction to Linear Algebra
An introductory linear algebra textbook with an emphasis on numerical methods.
Location:
Section 2.1, pages 31-38
Supplemental resources (the following are optional, but you may find them useful)
-Free-
→ Khan Academy: Linear Algebra
-Paid-
→ Multivariable Mathematics
A textbook on linear algebra and multivariable calculus with proofs.
Location:
Section 4.1, "Gaussian elimination and the theory of linear systems," pages 127-142
See also
- There are many techniques for solving linear systems that involve matrix operations such as: Computing the LU factorization is a computationally efficient method for solving linear systems