Khan Academy: Transpose of a Matrix: Rowspace and Left Nullspace

Review thee relationship between left nullspace, rowspace, column space and nullspace in this short video.

This videos offers a proof by induction that transposing a matrix does not change its determinant.

On this video tutorial students explore the rank of a matrix and the rank of the transpose.

Video first explains and gives examples of identity matrices. Then explains what an inverse matrix is and shows how to calculate the inverse of a 2x2 matrix. [14:14]

Transpose of a column vector. Matrix-matrix products using vectors in this video.

Transposes of sums and inverses are reviewed with this short video.

Showing that (transpose of A)(A) is invertible if A has linearly independent columns in this short video.

Video reviewing two fundamental subspaces of a matrix (null space and column space) and introducing two more (row space and left null space). Finds each of these subspaces for a specific 2x3 matrix and its transpose. Demonstrates that...

Video example of finding the inverse of a 3 by 3 matrix. Includes using expansion by minors to determine the determinant and finding the matrix of cofactors and adjugate or adjoint matrix. This video also appears in the strand Algebra:...

Video explains why a matrix is singular if its determinant is 0. Illustrates that when a matrix equation is built with a singular matrix, then there are no solutions because the system it represents is that of two parallel lines. Shows...