Nullspace of a 4×5 matrix via its SVD
Returning to this example, involving a matrix with row size 
and column size 
, and of rank 
. The nullspace is the span of the last 
columns of the 
matrix 
, with
![\[v_4:=\left(\begin{array}{l} 0 \\ 0 \\ 0 \\ 1 \\ 0 \end{array}\right), \quad v_5:=\left(\begin{array}{c} -\sqrt{0.8} \\ 0 \\ 0 \\ 0 \\ \sqrt{0.2} \end{array}\right)\]](https://ecampusontario.pressbooks.pub/app/uploads/quicklatex/quicklatex.com-d45fc5a1795a1ccff935d583a4f0ed59_l3.png "Rendered by QuickLaTeX.com")
We can check that 
.
Returning to this example, involving a matrix with row size and column size , and of rank . The nullspace is the span of the last columns of the matrix , with
We can check that .