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Fitting a Line using Least Squares #SoME2
The Least Squares method is widely used to fit curves to data. This is called Least Squares regression. This video shows how to solve the ordinary least squares minimization problem for 1 unknown and 2 unknowns. In...
TMW Media
A Matrix Defined
This program covers the very important topic of inconsistent and dependent systems in matrix math. Sometimes, a system of equations does not have a well-defined solution. For example, if we have two equations that represent two lines...
Khan Academy
Khan Academy: Linear Algebra: Least Squares Examples
An instructional video that works through a concrete example of finding the least squares approximation for a system of equations that has no solution. [18:50]
Khan Academy
Khan Academy: Linear Algebra: Least Squares Approximation
A video lesson explaining the least squares approximation for otherwise unsolvable matrix equations. Presents the motivation for why the least squares approximation is useful. Derives the formula for finding the least squares...
Khan Academy
Khan Academy: Linear Algebra: Row Space Solution to Ax = B Example
An instructional video that gives an example of how to find a solution to the equation Ax = b. In the example, the matrix A is 2 x 2. Shows that when the solution is a member of the row space of A for a given vector b, a member of the...
Khan Academy
Khan Academy: Linear Algebra: Matrices to Solve a Vector Combination Problem
Demonstrates how to find the appropriate combination of two given vectors in order to obtain a third given vector. This is done by representing the problem with a single matrix equation and solving that equation. [14:20]
Khan Academy
Khan Academy: Orthogonal Projections: Least Squares Approximation
A video lesson explaining the least squares approximation for otherwise unsolvable matrix equations. Presents the motivation for why the least squares approximation is useful. Derives the formula for finding the least squares approximation.
Khan Academy
Khan Academy: Linear Algebra: Row Space Solution to Ax = B Example
An instructional video that gives an example of how to find a solution to the equation Ax = b. In the example, the matrix A is 2 x 2. Shows that when the solution is a member of the row space of A for a given vector b, a member of the...
Khan Academy
Khan Academy: Orthogonal Complements: Rowspace Solution to Ax=b Example
An instructional video that gives an example of how to find a solution to the equation Ax = b. In the example, the matrix A is 2 x 2. Shows that when the solution is a member of the row space of A for a given vector b, a member of the...
Khan Academy
Khan Academy: Matrix Multiplication: Identity and Zero Matrix Equation
Models a problem where one must determine whether unknown matrices are zero or identity to make an equation true. [3:58]