Chapter 4 - Vector Spaces - 4.9 The Rank-Nullity Theorem - Problems - Page 330: 15

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$A$ is a $6 \times 4$ matrix, $n=4$ According to Rank- Nullity Theorem, we obtain: $rank (A)+nullity (A)=n \\ rank (A)=n-nullity (A)=4-0=4$ then $rowspace (A) \in R^4$ The only subspace of $R^1$ is $R^4$. Hence, $rowspace (A) = R^4$ Since $colspace (A)$ is a subspace of $R^6$, it is not possible to say that $colspace (A) =R^4$