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- Lecture 1: The Geometry of Linear Equations
- The matrix A (whose columns are u, v, w) times the column vector x (whose components are c, d, e) is the same as the combination cu + dv + ew of the three columns.
- Lecture 2: Elimination with Matrices
- Elimination works by creating a triangular matrix, which for a system of 3 equations and three variables gives us a new system of 3 equations that has one equation with only one variable, another with two variables, and the last with three variables. This system can then be easily solved.
- Lecture 3: Multiplication and Inverse Matrices
- When multiply matrices, A*B=C, the element in the i-th row and j-th column of the resultant matrix, C, is calculated by taking the dot product of the i-th row of A with the j-th column of B.
- Another way to view matrix multiplication: in A*B=C, each column of C is a linear combination of the columns of A. e.g.