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Returning to this example, involving a matrix with row size \(m=4\) and column size \(n=5\), and of rank \(r=3\). The nullspace is the span of the last \(n-r=2\) columns of the \(5 \times 5\) matrix \(V\):

\[\mathbf{N}(A) =\mathbf{span}\left(v_4, v_5\right),\]

with

\[v_4 := \left(\begin{array}{l}0 \\0 \\0 \\1 \\0\end{array}\right), \quad v_5 := \left(\begin{array}{c}-\sqrt{0.8} \\0 \\0 \\0 \\\sqrt{0.2}\end{array}\right).\]

We can check that \(A v_4 = A v_5 = 0\).