Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations. Also, functional analysis may be basically viewed as the application of linear algebra to spaces of functions. Linear algebra is also used in most sciences and engineering areas, because it allows modeling many natural phenomena, and efficiently computing with such models. ⭐️ Table of Contents ⭐ (0:00) Linear Algebra - Systems of Linear Equations (1 of 3) (16:20) Linear Algebra - System of Linear Equations (2 of 3) (27:55) Linear Algebra - Systems of Linear Equations (3 of 3) (47:18) Linear Algebra - Row Reduction and Echelon Forms (1 of 2) (54:49) Linear Algebra - Row Reduction and Echelon Forms (2 of 2) (1:4:10) Linear Algebra - Vector Equations (1 of 2) (1:14:05) Linear Algebra - Vector Equations (2 of 2) (1:24:54) Linear Algebra - The Matrix Equation Ax = b (1 of 2) (1:39:21) Linear Algebra - The Matrix Equation Ax = b (2 of 2) (1:44:48) Linear Algebra - Solution Sets of Linear Systems (1:57:49) Linear Algebra - Linear Independence (2:11:20) Linear Algebra - Linear Transformations (1 of 2) (2:25:10) Linear Algebra - Linear Transformations (2 of 2) (2:39:19) Linear Algebra - Matrix Operations (2:56:24) Linear Algebra - Matrix Inverse (3:12:17) Linear Algebra - Invertible Matrix Properties (3:24:24) Linear Algebra - Determinants (1 of 2) (3:44:40) Linear Algebra - Determinants (2 of 2) (4:04:28) Linear Algebra - Cramer's Rule (4:18:20) Linear Algebra - Vector Spaces and Subspaces (1 of 2) (4:48:30) Linear Algebra - Vector Spaces and Subspaces (5:13:13) Linear Algebra - Null Spaces, Column Spaces, and Linear Transformations (5:33:25) Linear Algebra - Basis of a Vector Space (5:59:43) Linear Algebra - Coordinate Systems in a Vector Space (6:15:41) Linear Algebra - Dimension of a Vector Space (6:26:35) Linear Algebra - Rank of a Matrix (6:50:09) Linear Algebra - Markov Chains (7:09:23) Linear Algebra - Eigenvalues and Eigenvectors (7:32:03) Linear Algebra - Matrix Diagonalization (7:49:08) Linear Algebra - Inner Product, Vector Length, Orthogonality