Khan Academy
Khan Academy: Linear Algebra: Matrix Product Examples
Video shows example of multiplying matrices. Includes explanation of the dimensions needed in order for matrices to be able to be multiplied. Connects to the composition of linear transformations. This video also appears in the strand...
Khan Academy
Khan Academy: Linear Algebra: Simplifying Conditions for Invertibility
A video lesson explaining that a transformation matrix is invertible if and only if it is a square identity matrix in reduced row echelon form. This video is also found in the strand Algebra: Matrices. [6:37]
Khan Academy
Khan Academy: Linear Algebra: Matrix Vector Products
Video starts with reviewing matrix notation. Defines multiplying a matrix by a vector and shows examples. Shows how the matrix-vector products can be interpreted as the dot product of column vectors with a matrix or as a weighted linear...
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: Linear Algebra: Linear Transformations: Scaling and Reflections
Video first reviews how to find the transformation matrix using the identity matrix. Shows how to write a transformation matrix that reflects over the y-axis and scales the y-coordinates by a factor of 2. [15:13]
Khan Academy
Khan Academy: Linear Algebra: More on Matrix Addition and Scalar Multiplication
Video reviews what was shown in the previous video that the sum of two linear transformations is the sum of their transformation matrices and the scalar multiple of a transformation is the scalar multiple of the transformation matrix....
Khan Academy
Khan Academy: Change of Basis: Alternate Basis Transformation Matrix Part 2
Showing that the transformation matrix with respect to basis B actually works. Brief point on why someone would want to operate in a different basis to begin with.
Khan Academy
Khan Academy: Using Orthogonal Change of Basis Matrix
Video defining an orthogonal matrix as a square matrix C whose columns form an orthonormal set.
Khan Academy
Khan Academy: Linear Transformation Examples
Expressing a Projection on to a line as a Matrix Vector prod
Khan Academy
Khan Academy: Changing Coordinate Systems to Help Find a Transformation Matrix
Changing our coordinate system to find the transformation matrix with respect to standard coordinates
Khan Academy
Khan Academy: Change of Basis: Alternate Basis Transformation Matrix Example
Example of finding the transformation matrix for an alternate basis.
Khan Academy
Khan Academy: Transpose of a Matrix: Transpose of a Vector
Transpose of a column vector. Matrix-matrix products using vectors in this video.
Khan Academy
Khan Academy: Invertible Change of Basis Matrix
Using an invertible change of basis matrix to go between different coordinate systems.
Khan Academy
Khan Academy: Linear Algebra: Inverting Matrices (Part 3)
Video shows using the Gauss-Jordan elimination method to determine the inverse of a 3 by 3 matrix. This video also appears in the strand Algebra: Matrices. [13:35]
Khan Academy
Khan Academy: Inverting Matrices: Inverting Matrices (Part 3)
Using Gauss-Jordan elimination to invert a 3x3 matrix.
Khan Academy
Khan Academy: Matrix Vector Products as Linear Transformations
Video first shows that matrix vector multiplication is another way to represent a transformation and then shows that matrix vector products are linear transformations.
Khan Academy
Khan Academy: Transformation Matrix With Respect to a Basis
Finding the transformation matrix with respect to a non-standard basis.
Khan Academy
Khan Academy: Transpose of a Matrix: Rowspace and Left Nullspace
Students explore transformations of matrices, rowspace and nullspace by watching a video tutorial.
Khan Academy
Khan Academy: Inverting Matrices: Inverting Matrices (Part 2)
Inverting a 3x3 matrix. This video includes using expansion of minors to determine the determinant and finding the matrix of cofactors and adjugate or adjoint matrix.
Khan Academy
Khan Academy: Linear Algebra: Rank(a) = Rank (Transpose of A)
A video lesson showing why the rank of a matrix is the equal to the rank of that matrix's transpose. [11:13]
Khan Academy
Khan Academy: Transpose of a Matrix: Transpose of a Matrix Product
This videos shows how to take the transpose of the product of two matrices.
Khan Academy
Khan Academy: Linear Algebra: Singular Matrices
Video explains why a matrix is singular if its determinant is 0. Relates why the inverse does not exist to solving systems of linear equations and vector combinations. This video also appears in the strand Algebra: Matrices. [14:27]
Khan Academy
Khan Academy: Inverting Matrices: Singular Matrices
Video explains why a matrix is singular if its determinant is 0. Relates why the inverse does not exist to solving systems of linear equations and vector combinations.
Khan Academy
Khan Academy: Orthonormal Basis: Orthogonal Matrices Preserve Angles and Lengths
This is a video showing that orthogonal matrices preserve angles and lengths.