Let \(v_1 , v_2 , v_3 \) be the column vectors of a non-zero 3× 3 real matrix A. Let \(a_1, a_2 , a_3 \) ∈ ℝ, not all zero, be such that ∑(aᵢ ⋅ vᵢ) = 0.
Then the system Ax = ∑(aᵢ ⋅ vᵢ) has:
1
more than one but only finitely many solutions
2
a unique solution
3
infinitely many solutions
4
no solution