Virtual Nerd
Virtual Nerd: How Do You Use Matrices to Translate a Figure?
Discover how to use a translation matrix to translate a figure on the coordinate plane. [6:25]
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: More Determinant Depth: Determinant as Scaling Factor
Video demonstrating that the area of a parallelogram that is the image of a rectangle under a transformation is equivalent to the absolute value of the determinant of the matrix whose column vectors generate the parallelogram.
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: Change of Basis: Alternate Basis Transformation Matrix Example
Example of finding the transformation matrix for an alternate basis.
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: 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: Linear Algebra: Inverting Matrices (Part 2)
Video example of finding the inverse of a 3 by 3 matrix. Includes using expansion of minors to determine the determinant and finding the matrix of cofactors and adjugate or adjoint matrix. This video also appears in the strand Algebra:...
Khan Academy
Khan Academy: Linear Algebra: Inverting Matrices (Part 2)
Video example of finding the inverse of a 3 by 3 matrix. Includes using expansion of minors to determine the determinant and finding the matrix of cofactors and adjugate or adjoint matrix. This video also appears in the strand Algebra:...
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: Null Space and Column Space: Column Space of a Matrix
A video introducing the column space of a matrix.
Khan Academy
Khan Academy: Transpose of a Matrix: Rank(a) = Rank(transpose of A)
On this video tutorial students explore the rank of a matrix and the rank of the transpose.
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: More Determinant Depth: Upper Triangular Determinant
A video lesson proving that the determinant of an upper triangular matrix is the product of the all of the entries along the main diagonal
Khan Academy
Khan Academy: Transformations and Matrix Multiplication: Matrix Product Examples
Students explore matrix transformations by examining an example of taking the product of two matrices.
Khan Academy
Khan Academy: Transpose of a Matrix: Determinant of Transpose
This videos offers a proof by induction that transposing a matrix does not change its determinant.
Khan Academy
Khan Academy: Basic Matrix Operations: Introduction to the Matrix
A video introducing matrices.
Khan Academy
Khan Academy: Orthogonal Complements: Dim(v) + Dim(orthogonal Complement of V)=n
Showing that if V is a subspace of Rn, then dim(V) + dim(V's orthogonal complement) = n
Khan Academy
Khan Academy: Finding the Determinant of a 3 X3 Matrix Method 2
This video shows how to find the determinant of a thre by three matrix.
Khan Academy
Khan Academy: Finding the Determinant of a 3 X3 Matrix Method 1
A video showing how to find the determinant of a 3 x 3 matrix.
Khan Academy
Khan Academy: Calculating Matrix of Minors and Cofactor Matrix
Inverting a 3x3 matrix then calculate the matrix of minors and the cofactor matrix.