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solving matrix over GF(2)

A = matrix(GF(2), 8, 8, [])
b = vector(GF(2), [0, 1, 1, 0, 1, 0, 1, 1])
y = vector(GF(2), [0, 0, 0, 0, 1, 0, 1, 1])
x = vector(GF(2), [1, 0, 0, 0, 0, 0, 0, 0])


If the matrix $A$ is unkown, we have $Ax+b = y$.

How can we solve the matrix $A$?