Let c1.....cn be scalars, not all zero

Let c1.....cnc1.....cn be scalars, not all zero, such that ∑ni=1ciai∑i=1nciai = 0 where aiai are column vectors in RnRn.

Consider the set of linear equations

Ax=bAx=b

where A=[a1.....an]A=[a1.....an] and b=∑ni=1aib=∑i=1nai. The set of equations has

(A) a unique solution at x=Jnx=Jn where JnJn denotes a nn-dimensional vector of all 1.

(B) no solution

(C) infinitely many solutions

(D) finitely many solutions

3Comments
Sumit Verma @sumitkgp
25 Apr 2017 11:54 pm

Can you please correct your question ? 

shweta @shweta1920
26 Apr 2017 11:32 am

?what to correct? ? .. its a gate 2017 question

Sumit Verma @sumitkgp
26 Apr 2017 12:09 pm

@shweta1920 Please read this question once.