Let c 1 … c n be scalars, not all zero, such that \sum ↙\stackrel{n}{i = 1}⁡c_{i}a_{i} = 0 where a i are column vectors in R n . Consider the set of linear equations Ax = b where A = [a_{1}\ldotsa_{n}] \:and\:b = \sum ↙\stackrel{n}{i = 1}⁡a_{i} The set of equations has

Correct Answer is : infinitely many solutions

a unique solution at x = J n where J n denotes a n-dimensional vector of all 1

GATE Computer Science (CS) 2017 Shift 1 Solved Paper

Question : 13 of 65

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Let c₁ … c_n be scalars, not all zero, such that

∑ ↙{i = 1}↖{n}⁡c_{i}a_{i} = 0

where a_i are column vectors in Rⁿ. Consider the set of linear equations
Ax = b
where A =

[a_{1}…a_{n}] \:and\:b = ∑ ↙{i = 1}↖{n}⁡a_{i}

The set of equations has

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