Question: LinearSolve taking too long to compute

Hello everyone,

I am trying to solve a system of six equations through a matrix and a vector. The matrix is 6x6, so the function "LinearSolve" should find a solution 

The matrix is

Matrix(6, 6, [[1., -1., 1., -1., 1., -1.], [1., 1., 1., 1., 1., 1.], [-2., 1.618033989, 30.94427190, -153.8246851, 371.1559479, -572.9674774], [-2., 0.6180339876, 22.94427191, -41.15905356, -37.04759741, 149.3606798], [-2., -0.6180339876, 13.05572810, 22.82468509, -20.15594802, -81.03252254], [-2., -1.618033989, 5.055728096, 28.15905368, 68.04759752, 104.6393203]])

and the vector associated with the system is

Vector[column](6, [-1/3, -1, 0, 0, 0, 0])

I am trying to solve this system with

a := LinearSolve(M3, v);

but it stays evaluating.

I have solved a similar system (5x5) with this function (LinearSolve) and it took less than a second, so I dont understand why it takes so long in this case.

Thank you in advance.