Column Matrix Teacher Resources

Purplemath gives the fundamentals of matrices. Begins with linear equations of three variables and shows the corresponding matrix. Discusses the augmented and coefficient matrix formed from the equation. The size of a matrix and special...

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 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 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 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 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...

A video introducing the column space of a matrix.

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....

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

This video calculates the null space of a matrix.

Video defining an orthogonal matrix as a square matrix C whose columns form an orthonormal set.

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

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

Finding the determinant by going along other rows or columns

A video lesson proving that the product of a matrix and its transpose is invertible if all of the columns of the originial matrix are linearly independent. [12:34]

A video demonstrating working with matrices.

Video builds upon the column spaces and null spaces of the 2x3 matrix and its transpose found in the previous video. Uses them to explain some relationships between the four fundamental subspaces, namely that the orthogonal complement of...

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 reviews what the null space of a matrix is and how to calculate it, then relates it to linear independence. Shows that if the vectors are linearly independent then the null space is the zero vector. Also shows that if the null...

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...

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...

Video demonstrating that the dot product of two vectors is equivalent to the matrix product of the transpose of the first vector times the second vector. Uses this idea to show that the dot product of a matrix-vector product and another...

Video demonstrating that the area of a parallelogram created by graphing the column vectors of a 2x2 matrix is the equivalent to the absolute value of the determinant of the matrix. Pythagorean theorem, in conjunction with calculating a...

A video lesson describing how the determinants for larger matrices can be found using cofactor expansion on any row or column. Illustrates that it is helpful to choose rows or columns with zeros in order to simplify the computations....