Linear Algebra (Full Course) (Matrices, Inverse, Vector Space, Subspace) in 14 Hours (Part 1 of 2)

Thanks for watching and please subscribe for more content.

PART 1: Systems of Linear Equations and Matrices
00:00:00 Intro to linear equations
00:02:38 General form of systems of linear equations
00:04:22 Solutions to linear systems (2 unknowns)
00:05:26 Solutions to linear systems (3 unknowns)
00:07:38 Worked examples on solutions to linear systems
00:14:49 Augmented matrices
00:17:05 Row operations on augmented matrices
00:24:22 Row echelon forms
00:30:03 Worked examples on row echelon forms
00:34:34 Gauss-Jordan vs Gaussian elimination
00:42:59 Homogeneous linear systems
00:47:08 Gaussian elimination with back substitution
00:51:34 Matrix notation, vectors and size
00:54:17 Basic matrix operations (addition, subtraction, equality, scalar product, trace)
00:58:20 Matrix multiplication
01:03:50 Partitioned matrices
01:08:52 Matrix products and linear combinations
01:10:59 Matrix transpose
01:13:26 Intro to matrix inverse
01:19:13 Inverse of matrix products
01:21:24 Powers of matrices
01:24:48 Inverse of a 3x3 matrix by Gauss-Jordan elimination
01:30:09 Solving linear systems by matrix inversion
01:31:54 Inverse and powers of diagonal matrices
01:34:15 Triangular matrices, and their inverse and transpose
01:38:40 Symmetric matrices, inverse and transpose
PART 2: Matrix Determinants and Inverse
01:40:24 Determinant of a matrix
01:49:09 Determinant by Gaussian elimination
01:53:25 Inverse using the adjoint matrix
01:57:23 Cramer's rule
PART 3: Extending Vectors from 3-Space to n-Space
02:02:13 Vectors in 2D and 3D space
02:14:48 Vectors in n-space
02:25:02 Norm of a vector in n-space and standard unit vectors
02:32:39 Dot product in n-space
02:53:11 Orthogonality and projection using the dot product
03:04:00 Cross product and triple scalar product, area and volume
PART 4: Real Vector Spaces, Fundamental Matrix Spaces, Matrix Transformations and Operators
03:25:09 Real vector spaces
03:44:21 Vector subspaces, span and linear combinations
04:09:13 Linearly independent vectors, linear independence, examples
04:24:20 Basis for a vector space, coordinate vectors
04:45:13 Dimension of a vector space
04:54:47 Change of basis, mapping and the transition matrix
05:21:32 Row space, column space and null space
05:52:22 Rank and nullity of a matrix
06:11:08 Matrix transformations, operators (projection, reflection, rotation and shear)
06:42:11 Compositions of matrix transformations, one-to-one, inverse of operator