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$\begingroup$ This isn't in the form $Ax = 0$, so the zero vector is the only solution iff $A$ is invertible statement doesn't apply here. In fact, $Ax = b$ has the trivial

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You are not solving AX=0. But AᵀX=0. Because the equation you gave was np.array(x) @ A. x is a 1D array. Which means that it is treated as a line or as a column

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