Search
- Filter Results
- Location
- Classification
- Include attachments
- https://math.libretexts.org/Bookshelves/Linear_Algebra/Supplemental_Modules_(Linear_Algebra)/2%3A_Determinants_and_InversesTo find the determinant of a matrix we use the operations to make the matrix triangular and then work backwards. Since this matrix has \(\frac{1}{2}\) the determinant of the original matrix, the deter...To find the determinant of a matrix we use the operations to make the matrix triangular and then work backwards. Since this matrix has \(\frac{1}{2}\) the determinant of the original matrix, the determinant of the original matrix has If \(A\) is a square matrix then the inverse \(A^{-1}\) of \(A\) is the unique matrix such that To find the inverse of a matrix, we write a new extended matrix with the identity on the right.
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/03%3A_DeterminantsThis page explains the importance of determinants in square matrices, covering their properties, applications, and geometric interpretations. It discusses their relation to matrix inverses and Cramer'...This page explains the importance of determinants in square matrices, covering their properties, applications, and geometric interpretations. It discusses their relation to matrix inverses and Cramer's Rule, emphasizes the effects of row operations on determinants, and includes examples for clarity. Furthermore, it highlights the geometric interpretation of determinants as volumes, enhancing comprehension of their defining properties and relevance in multivariable calculus.
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/02%3A_Matrices/2.03%3A_Elementary_MatricesThis page covers the concept of elementary matrices, which are derived from the identity matrix using row operations. It details how these matrices are key in finding the inverse of matrices and expre...This page covers the concept of elementary matrices, which are derived from the identity matrix using row operations. It details how these matrices are key in finding the inverse of matrices and expresses a matrix as a product of elementary matrices. Properties of invertible matrices are discussed, including the conditions that an \(n \times n\) matrix must meet to be invertible, emphasizing the significance of row operations.
