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Nullspace of a 4×5 matrix via its SVD

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.

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