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by vlasev
2224 days ago
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Take a 3x3 matrix A for example. Then det(A) is the volume of the parallepiped formed by the row vectors. If one vector is a linear combination of the other two, this means that the vectors lie in a plane, which has volume 0 in 3D, so det(A) = 0. Since we have a plane in 3D, this means A can't express all vectors in 3D, so it's not invertible. This generalizes to any dimension. |
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