MATH 104 –Linear Algebra
Instructor: Mohamed Abdou Mahran Kasem, Ph.D.
NU –EAS
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Linear Algebra: Determinants of Matrices, Lecture notes of Linear Algebra
The concept of determinants of matrices in linear algebra. It explains how to find the determinant of a matrix of order 2, the definition of the determinant of a 2x2 matrix, and how to find the minors and cofactors of a matrix. It also covers expansion by cofactors and determinants using elementary row operations. The document ends with examples of properties of determinants.
Typology: Lecture notes
2021/2022
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MATH 104 – Linear Algebra
Instructor: Mohamed Abdou Mahran Kasem, Ph.D. NU – EAS
Lecture code of ethics o Attendance is mandatory o No cell phones o No side talks o Write as much as you can
Lecture Contents ➢ Determinant of matrices ➢ Determinant Applications
Introduction
- Every square matrix can be associated with a real number called its determinant.
- Historically, the use of determinants arose from the recognition of special patterns that occur in the solutions of systems of linear equations.
- For instance, the general solution of the system
Definition
Definition
Minors and Cofactors of a Matrix
Minors and Cofactors of a Matrix
Minors and Cofactors of a Matrix
Example
Expansion by cofactors
Expansion by cofactors
Determinants using Elementary Row Operations
Determinants using Elementary Row Operations