Rank–nullity dimension count

MediumLinear Algebra~3m

A linear map $A:\mathbb{R}^{7}\to\mathbb{R}^{4}$ (a $4\times7$ matrix) has a null space (solution set of $Ax=0$ ) of dimension $3$ . What is the dimension of its column space (its rank)?

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Rank–nullity: $\operatorname{rank}+\operatorname{nullity}=$ number of columns (domain dimension).
Domain is $\mathbb{R}^{7}$ , so rank $=7-3$ .

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Rank–nullity dimension count

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