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Is it homework ? Here are some hints:

• if you remove the first element to all elements of an affine space, you get a vector space
• this vector space has a basis
• turn this basis into a matrix M (by columns)
• the lines of the matrix A you are looking for are a basis of the right kernel of M (write the things down on a paper to get convinced)
• you get the b by plugging any element of your affine space in the equation

Is it homework ? Here are some hints:

• if you remove the first element to all elements of an affine space, you get a vector spacespace (see VectorSpace and its vector_space_span method)
• this vector space has a basis
• turn this basis into a matrix M (by columns)
• the lines of the matrix A you are looking for are a basis of the right kernel of M (write the things down on a paper to get convinced)
• you get the b by plugging any element of your affine space in the equation