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Khan Academy
Khan Academy: Linear Algebra: Dimension of the Column Space or Rank
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....
Khan Academy
Khan Academy: Orthogonal Complements: Orthogonal Complement of the Nullspace
A video lesson illustrating that the orthogonal complement of the nullspace is equal to the row space and vice versa.
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: Orthogonal Complements: Orthogonal Complements
Video introducing the orthogonal complement of a subspace and showing that it is also a subspace. Proves that the null space of a matrix is equivalent to the orthogonal complement of its row space by showing that every member of the null...
Khan Academy
Khan Academy: Linear Algebra: Column Space of a Matrix
Video defines the column space a a linear combination of the column vectors and relates it to span. Shows that the column space is a valid subspace. Shows several ways to interpret a column space. This video also appears in the strand...
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: Linear Algebra: Visualizing a Column Space as a Plane in R3
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...
Khan Academy
Khan Academy: Linear Algebra: Visualizing a Column Space as a Plane in R3
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...
Khan Academy
Khan Academy: Calculating the Null Space of a Matrix
This video calculates the null space of a matrix.
Khan Academy
Khan Academy: Showing Relation Between Basis Cols and Pivot Cols
This video shows that linear independence of pivot columns implies linear independence of the corresponding columns in the original equation.
Khan Academy
Khan Academy: Visualizing a Column Space as a Plane in R3
A video demonstrating working with matrices.