Video shows an example of proving that a particular linear combination of 3 vectors in R3 spans R3. Relates this to linearly independent and linearly dependent vectors. [16:53]

Video expands the examples of linearly independent and linearly dependent vectors shown in the previous video to give a formal definition of linearly dependent vectors. Shows a proof of the definition and then gives an example of using...

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 explains what linearly dependent vectors and linearly independent vectors are. Shows visual representations to help explain the concept and relates it to the span of the linear combination of the vectors. [15:46]

Video shows an example of proving a particular linear combination of 3 vectors in R3 spans R3. Relates this to linearly independent and linearly dependent vectors. [16:53]

Video expands the examples of linearly independent and linearly dependent vectors shown in the previous video to give a formal definition of linearly dependent vectors. Shows a proof of the definition and then gives an example of using...

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...