Chapter Overview
The chapter ‘Determinants’ introduces students to an important numerical value associated with square matrices. Determinants play a significant role in linear algebra and are used to solve systems of linear equations using Cramer's Rule, determine matrix invertibility, and understand the geometric interpretation of area and volume. This chapter covers the definition of determinants, expansion by minors and cofactors, properties, applications, and the concept of adjoint and inverse of a matrix.
Important Keywords
- Determinant: A scalar value derived from a square matrix, denoted as det(A) or |A|.
- Minor: Determinant of a smaller matrix formed by deleting one row and one column.
- Cofactor: Minor of an element with a sign based on its position.
- Adjoint: Transpose of the matrix of cofactors.
- Singular Matrix: A matrix with determinant equal to zero.
- Non-Singular Matrix: A matrix with a non-zero determinant.
- Inverse of a Matrix: A⁻¹ exists if det(A) ≠ 0.
- Cramer’s Rule: A method to solve linear equations using determinants.
Detailed Notes
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