About Linear Algebra Full Course | Step-by-Step Lessons, Examples & Applications

Basis for the Null Space and Column Space via Row Reduction to RREF Solving Homogeneous Systems and Vector Parametric Forms Determining a Basis: Linear Independence and Spanning via Determinant or Echelon Form Geometric Linear Transformations in R2: Reflection, Rotation, Shear, and Projection Matrices Matrix Equations Ax=b: Solvability for All b via Column Space Spanning Determinant Calculation: Cofactor Expansion, Sarrus' Rule, and Triangular Matrices Mathematics in general Singular Value Decomposition via Eigenvalue Decomposition of A^TA and AA^T Mathematics for nonmathematicians (engineering, social sciences, etc.) Solving Systems of Linear Equations Using Elementary Row Operations Gram-Schmidt Process and QR Factorization Solving Traffic Flow and Balancing Chemical Equations in Linear Algebra