MATH 1107 Lecture : Lesson 13b -Linear Dependence and Linear Independence.pdf
Document Summary
Where c1, c2, c3, , cn are not all zero (non trivial) solution. t i i l ti l) t ll. Proof: v we call them linearly dependent when: v v v v1, v2, v3, , vn, we call them linearly dependent when: c1v1+c2v2+c3v3+ +cnvn=0. 1 c i c i vc i i c n c i c n c i c. 3 c i c i c i vc nn. 1 v i v i v i v i v n v n v. 1 v i c i c i v i. We can repeat this process until we have no free variables once we have no free. From the previous theorem ax=0 must have at least one free variable as we could. If there are none, we are done as the set is linearly independent we are done as the set is linearly independent. Thus we have: i bl ( 3 di h t t f l.