Section 10.3 Determinants
Determinants
Remark: Determinants are scalars related to square matrices. They kind of serve the role
as the “abosolute” value of matrices, although determinants could be a negative number.
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Determinants and Cramer's Rule in Linear Algebra, Study notes of Mathematics
This section covers the concept of determinants as scalars related to square matrices, their role as the 'absolute' value of matrices, and cramer's rule for solving linear systems. However, it's noted that cramer's rule is not commonly used in practice due to its computational cost.
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Section 10.3 Determinants
Determinants
Remark: Determinants are scalars related to square matrices. They kind of serve the role as the “abosolute” value of matrices, although determinants could be a negative number.
Exercise 1
Exercise 2
Cramer’s Rule
Remark: Cramer’s rule is a formally elegant way to solve a linear system. But, in real life, people do not use it to solve linear system because it is computationally costly.
- Exercise
- Exercise
Determinants of Larger Square Matrices
In order to generalize the determinants to higher order matrices, we need to use another definition for the determinants. Interested readers may google or wiki for detailed definition and illustration.