Exercise20.4

In class we proved that \(\range(A)=\Span(u_1, u_2, \dots, u_r),\) where \(r\) is the number of nonzero singular values of \(A\text{.}\) Now prove that

\begin{equation*} \Null(A)=\Span(v_{r+1},\dots, v_n). \end{equation*}
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