Video first gives examples of finding the column space and null space of a matrix. Shows how to determine if the column space is a basis. Gives an example of finding the basis of the column space if the column space is not already a...

Video first reviews how to find the basis for the column space of a matrix using the reduced row echelon form. Proves that the basis for the column space using the reduced row echelon form method spans the column space. Uses this and the...

Video shows how to find the basis and dimension of the column space by finding its reduced row echelon form and using the columns corresponding to the pivot columns as the basis. Explains that rank is the dimension of the column space....

Video reviews how to find a basis for the column space and talks about how to find it more efficiently using reduced row echelon form. Shows a visualization of the column space in R3 as a plane. Shows two methods to determine the...

Video shows proof that any basis of a particular subspace has the same number of elements. Leads up to give the definition of dimension. This video also appears in the strand Algebra: Matrices. [21:25]

Video explains what a basis for a vector subspace is and its criteria: the vectors must span the subspace and be linearly independent. Also gives an informal definition of basis as the minimum set of vectors that spans the subspace....

Video shows proof that any basis of a particular subspace has the same number of elements. Leads up to give the definition of dimension. This video also appears in the strand Algebra: Matrices. [21:25]

Video shows proof that any basis of a particular subspace has the same number of elements. Leads up to give the definition of dimension.