An examination of the Manufacturing Industry as a career field.

- Subject:
- Manufacturing
- Material Type:
- Lecture
- Author:
- Robert Speckert
- Date Added:
- 09/17/2019

Only Sharing Permitted

CC BY-NC-ND
An examination of the Manufacturing Industry as a career field.

- Subject:
- Manufacturing
- Material Type:
- Lecture
- Author:
- Robert Speckert
- Date Added:
- 09/17/2019

Unrestricted Use

CC BY
One of a set of toolkits to support student development and personal reflection. Produced by students for students.

- Subject:
- Education
- Material Type:
- Interactive
- Lecture
- Provider:
- University of British Columbia
- Provider Set:
- Learning Commons
- Author:
- UBC Learning Commons Web Team
- Date Added:
- 08/31/2012

Conditional Remix & Share Permitted

CC BY-NC-SA
This 10-minute video lesson looks at Determinants: Finding the determinant of a 3x3 matrix.

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
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.

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 15-minute video lesson sees that orthonormal bases make for good coordinate systems.

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
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.

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
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.

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Salman Khan
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 25-minute video lesson introduces the idea of an angle between two vectors.

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Salman Khan
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 10-minute video lesson looks at what happens to the determinant when we perform a row operation.

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 13-minute video lesson looks at the determinant when a row is multiplied by a scalar.

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
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).

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
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.

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 20-minute video lesson shows how to view the determinant of the transformation matrix as a scaling factor of regions.

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 14-minute video lesson shows the proof by induction that transposing a matrix does not change its determinant.

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 9-minute video lesson shows how to find the determinant by going along other rows or columns.

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 19-minute video lesson provides dot and cross product comparison and Intuition.

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Salman Khan
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 8-minute video lesson looks at the determinant of a matrix with duplicate rows.

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This video shows an example using orthogonal change-of-basis matrix to find transformation matrix

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 7-minute video lesson gives an example of finding the transformation matrix for the projection onto a subspace with an orthonormal basis.

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 18-minute video lesson shows how to figure out the formula for a 2x2 matrix. And it defines the determinant.

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 13-minute video lesson uses Gram-Schmidt to find an orthonormal basis for a plane in R3.

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
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.

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 3-minute video lesson looks at the orthogonal complement of the nullspace and left nullspace.

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This video shows how to find that the orthogonal complement of the orthogonal complement of V is V

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 22-minute video lesson looks at orthogonal Complements as subspaces.

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This video shows that orthogonal matrices preserve angles and lengths

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 16-minute video lesson looks at projections onto subspaces with orthonormal bases.

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 17-minute video lesson looks at projections onto subspaces.

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 17-minute vidoe lesson shows proof of the Cauchy-Schwarz Inequality.

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Salman Khan
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 11-minute video lesson proves the "associative," "distributive," and "commutative" properties for vector dot products.

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Salman Khan
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
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.

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 7-minute video lesson gives an alternative (short cut) for calculating 3x3 determinants (Rule of Sarrus).

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 9-minute video lesson shows how to calculate a 4x4 determinant by putting in in upper triangular form first.

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 19-minute video lesson finds an orthonormal basis for a subspace using the Gram-Schmidt Process.

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 8-minute video lesson looks at the determinant of an upper triangular matrix.

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 9-minute video lesson provides definitions of the vector dot product and vector length.

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Salman Khan
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 19-minute video lesson proves the triangle inequality for vectors in Rn.

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Salman Khan
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This video shows that if V is a subspace of Rn, then dim(V) + dim(V's orthogonal complement) = n

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 19-minute video lesson shows how to define the determinant for nxn matrices. And it provides an exampled of a 4x4 determinant.

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 14-minute video lesson provides an Introduction to linear transformations.

- Subject:
- Algebra
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Salman Khan
- Date Added:
- 02/20/2011