Nullity of a concrete matrix

MediumLinear Algebra~4m

What is the dimension of the null space of $A = \begin{pmatrix} 1 & 2 & 1 & 0 \\ 2 & 4 & 2 & 1 \\ 3 & 6 & 3 & 1 \end{pmatrix}$ (a map $\mathbb{R}^4 \to \mathbb{R}^3$ )?

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Row-reduce to find the rank first - the rows are not all independent.
$\dim(\text{null}) = 4 - \text{rank}$ .

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Nullity of a concrete matrix

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