Khan Academy
Khan Academy: Linear Algebra: Linear Combination and Spans
Video explains what a linear combination is and gives a concrete example of a linear combination of two vectors in two dimensions. Linear combinations are then extended to introduce spans of vectors. Shows a proof that two non-parallel...
Khan Academy
Khan Academy: Linear Algebra: Basis of a Subspace
Video explains what a basis for a vector subspace is and its criteria: the vectors must span the subspace and be linearly independent. Also gives an informal definition of basis as the minimum set of vectors that spans the subspace....
Khan Academy
Khan Academy: Linear Algebra: Span and Linear Independence Example
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]
Khan Academy
Khan Academy: Linear Algebra: More on Linear Independence
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...
Khan Academy
Khan Academy: Linear Algebra: Linear Combination and Spans
Video explains what a linear combination is and gives a concrete example of a linear combination of two vectors in two dimensions. Linear combinations are then extended to introduce spans of vectors. Shows a proof that two non-parallel...
Khan Academy
Khan Academy: Linear Combinations and Spans: Linear Combinations and Span
Video explains what a linear combination is and gives a concrete example of a linear combination of two vectors in two dimensions. Linear combinations are then extended to introduce spans of vectors.