Linear Independence Definition (1)If v1,v2,...,Un satisfy a nontrivial dependence relation then they are said to be linearly dependent. (2)v1,v2,...,n are said to be linearly independent if they are not linearly dependent. So,v1,v2,...,Un are linearly independent if C11+C22+..+Cnvn=0 →all the c's ae zero. Exercise:Show e1,e2,...,en are linearly independent in R". 4口，+心，在+4生，定QCLinear Independence Definition (1) If v1, v2, . . . , vn satisfy a nontrivial dependence relation then they are said to be linearly dependent. (2) v1, v2, . . . , vn are said to be linearly independent if they are not linearly dependent. So, v1, v2, . . . , vn are linearly independent if c1v1 + c2v2 + . . . + cnvn = 0 =⇒ all the ci ’s ae zero. Exercise: Show e1, e2, . . . , en are linearly independent in R n