Advanced Engineering Mathematics, Lecture 1.2: Linear independence and spanning sets

Advanced Engineering Mathematics, Lecture 1.2: Linear independence and spanning sets

In any vector space V, a set S is linearly independent if there are no non-trivial ways to write the zero vector as a linear combination of elements in S. In contrast, the set S spans V if every vector in v can be expressed as a linear combination of elements in S. Finally a set B is a basis for V if it is (i) linearly independent, and (ii) spans V. Think of this as the "Goldilocks condition": B is big enough to generate V, but not too big that it has any redundancies. An equivalent definition of of basis is that every vector in V can be written *uniquely* as a linear combination of elements in B.

[vikumvichakshanaFsv]

Sir, I have small question about in 22.27 part, In that part you say c1*cost +c2 *sin t =0 should c1=c2=0, but sir, we can select t=45degree in firstcodrent and c1=-1 and c2=1 ' ifthatcase we canget zero answer for that statement without c1=c2 =0, cam you explane that?🤨