MATH125 Lecture Notes - Lecture 15: Linear Independence, Diagonal Matrix, Augmented Matrix

• School: University of Alberta
• Department: Mathematics
• Course: MATH125
• Professor: Nikita

Document Summary

, vk is linearly dependent if there exist scalars c1, c2, . , ck at least one of which is not zero such that c1v1 + c2v2 + + ckvk = 0. A set of vectors that are not linearly dependent is called linearly inde- pendent. In the de nition of linearly dependence the requirment that at least one of the scalars c1, . , ck must be nonzero allows the possi- bility that some may be zero. 1 ] are linearly dependent since at least one of the scalars 1, 2 and 0 is nonzero. , vk in rn are linearly dependent if and only if at least one of them can be expressed as a linear combination of the others. Any set of vectors containing the zero vector is linearly dependent. Indeed if the set is 0, v2, v3, .