dse 2011

[shikha]

suppose {V1,V2,V3.....Vn} is a set of linearly Dependent vectors, none of them being the zero vector.Suppose C1,C2,C3,..Cn are scalers, not all zero, such that
 E(summation) CiVi = 0 for i = 1, 2, 3....n.
Then  the minimum number of non- zero scalers is

A) 1
B) 2
C) n-1
D) cannot be determined

Plz tell me which option is correct??

[komal]

it depends on relation between these vector , the min. no. varies from 2 to n depending on relationship, so answer should be cannot be determined i.e.(d)

[Amit Goyal]

total number of non-zero scalars cannot be determined but minimum can be, it is 2

[s]

can someone please upload the DSE 2011 paper...

[ritu]

why minimum number is 2 sir????why not 1???

[duck]

Hi Ritu.. :)

Suppose, we have 3 non zero linearly dependent vectors such that:
c1*v1 + c2 *v2 + c3*V3 =0

=> v1 = -(c2/c1)*v2 -(c3/c1)*v3

Now, if you take only one scalar(let it be c1) to be non zero and other two (c2 and c3) be zero
then, v1 = 0 but v1 is a non zero vector which is a contradiction.
Hence, minimum number is 2 and not 1.

[ritu]

thanx duck....i got it:)