This 16-minute video lesson looks at projections onto subspaces with orthonormal bases.
This 17-minute video lesson looks at projections onto subspaces.
This 17-minute vidoe lesson shows proof of the Cauchy-Schwarz Inequality.
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.
This 7-minute video lesson gives an alternative (short cut) for calculating 3x3 determinants (Rule of Sarrus).
This 9-minute video lesson shows how to calculate a 4x4 determinant by putting in in upper triangular form first.
This 19-minute video lesson finds an orthonormal basis for a subspace using the Gram-Schmidt Process.
This 8-minute video lesson looks at the determinant of an upper triangular matrix.
This 9-minute video lesson provides definitions of the vector dot product and vector length.
This 19-minute video lesson proves the triangle inequality for vectors in Rn.
This video shows that if V is a subspace of Rn, then dim(V) + dim(V's orthogonal complement) = n
This 19-minute video lesson shows how to define the determinant for nxn matrices. And it provides an exampled of a 4x4 determinant.
This 14-minute video lesson provides an Introduction to linear transformations.
This is a Calculus I interactive textbook with modules curated and created on The Ohio State University's Ximera platform.
The software upon which this interactive textbook was built is licensed under a GNU General Public License v.2.0, and therefore this resource caries the same license. Pursuant to this license, no warranties are made.
Review the license terms at https://github.com/XimeraProject/server/blob/master/LICENSE
This is a Calculus II interactive textbook with modules curated and created on The Ohio State University's Ximera platform.
The software upon which this interactive textbook was built is licensed under a GNU General Public License v.2.0, and therefore this resource caries the same license. Pursuant to this license, no warranties are made.
Review the license terms at https://github.com/XimeraProject/server/blob/master/LICENSE
My Math GPS: Elementary Algebra Guided Problem Solving is a textbook that aligns to the CUNY Elementary Algebra Learning Objectives that are tested on the CUNY Elementary Algebra Final Exam (CEAFE). This book contextualizes arithmetic skills into Elementary Algebra content using a problem-solving pedagogy. Classroom assessments and online homework are available from the authors.
From the preface, "These are notes for a course in precalculus, as it is taught at New York City College of Technology - CUNY (where it is offered under the course number MAT 1375). Our approach is calculator based. For this, we will use the currently standard TI-84 calculator, and in particular, many of the examples will be explained and solved with it. However, we want to point out that there are also many other calculators that are suitable for the purpose of this course and many of these alternatives have similar functionalities as the calculator that we have chosen to use. An introduction to the TI-84 calculator together with the most common applications needed for this course is provided in appendix A. In the future we may expand on this by providing introductions to other calculators or computer algebra systems."
This 15-minute video lesson gives an example involving the preimage of a set under a transformation. It also gives a definition of kernel of a transformation.