One of a set of toolkits to support student development and personal reflection. Produced by students for students.
This 22-minute video lesson shows another example of a projection matrix. It shows how to figure out the transformation matrix for a projection onto a subspace by figuring out the matrix for the projection onto the subspace's orthogonal complement first.
This 3-minute video lesson is a correction of last video showing that the determinant when one row is multiplied by a scalar is equal to the scalar times the determinant.
This 14-minute video lesson shows how to determine the equation for a plane in R3 using a point on the plane and a normal vector.
This 17-minute video lesson looks at the determinant when one matrix has a row that is the sum of the rows of other matrices (and every other term is identical in the 3 matrices).
This 22-minute video lesson realizes that the determinant of a 2x2 matrix is equal to the area of the parallelogram defined by the column vectors of the matrix.
This video shows an example using orthogonal change-of-basis matrix to find transformation matrix
This 7-minute video lesson gives an example of finding the transformation matrix for the projection onto a subspace with an orthonormal basis.
This 12-minute video lesson looks at sets and bases that are orthonormal -- or where all the vectors have length 1 and are orthogonal to each other.
This 11-minute video lesson proves the "associative," "distributive," and "commutative" properties for vector dot products.
This 27-minute video lesson shows that any member of Rn can be represented as a unique sum of a vector in subspace V and a vector in the orthogonal complement of V.