My attempt:
rank(XY) = dim(C(XY))
rank(X) = dim(C(X))
Therefore, dim(C(XY)) = dim(C(X))
Therefore, C(XY) is a subset of C(X)
Therefore, C(XY) = C(X)
2026-04-07 00:23:35.1775521415
If rank(XY) = rank(X), show that the column space C(XY) = C(X)
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