Linear dependence and independence Ill 3. The vectors(1,)and(1, 2) are linearly independent, since if a(1)+(2)-(8) then C1+C2=0 +2c2=0 and the only solution to this system is c1=0, c2=0. Thus,fⅵ,v,……, n are linearly endent, then no vector can be expressed as a linear combination of the rest vectors. Equivalently c1Ⅵ+c2v+…+Cnvn=Q implies that C1=0=C2=Linear dependence and independence III 3. The vectors (1, 1)T and (1, 2)T are linearly independent, since if c1  1 1  + c2  1 2  =  0 0  then c1 + c2 = 0 c1 + 2c2 = 0 and the only solution to this system is c1 = 0, c2 = 0. Thus, if v1, v2, · · · , vn are linearly independent, then no vector can be expressed as a linear combination of the rest vectors. Equivalently c1v1 + c2v2 + · · · + cnvn = 0 implies that c1 = 0 = c2 = · · · = cn. () May 3, 2006 3 / 40