Question: What did I wrong: Determine the complete solution to the corresponding homogeneous equation system?

I tried to solve this problem. 

It is a Maple TA question, but I get my solution wrong.

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Question:

There is given a linear equation system consisting of two equations with four unknowns.

Determine the complete solution to the corresponding homogeneous equation system. The answer must be given atparametrised vector shape.

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My solution:

with(LinearAlgebra)

A := Matrix(2, 4, [[-1,-2,1,2],[2,-2,-1,1]])

C := Vector(2, [0, 0])

LinearSolve(A, C) =>

Vector(4, {(1) = 4*_t0[2]-3*_t0[4], (2) = _t0[2], (3) = 6*_t0[2]-5*_t0[4], (4) = _t0[4]}) 

Now I set, (it is just some random numbers):

_t0[2] := 0

_t0[4] := 1

And now I get

Vector(4, [-3,0,-5,1])

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Malpe TA answer

Maple TA say that my answer is wrong. And it suggest this answer:

A correct answer is any linear combination of vectors in the volume

{Vector(4, {(1) = 1/3, (2) = 5/6, (3) = 0, (4) = 1}), Vector(4, {(1) = 2/3, (2) = 1/6, (3) = 1, (4) = 9})}

There are many other correct answers.

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Any suggestion how I can solve this?

/LilleLars