Solve Ax=0 using Single Value Decomposition

Question

Trying to solve Ax=o when $A=\begin{bmatrix}2&1&-1\\1&2&1\\ \end{bmatrix}$ using single value decomposition. I have the s,v,u and was thinking that x was as simple as $x=s*s^t$ but that didn't seem to work when I checked it. I know that when Ax=b that $x=(A^tA)^{-1}b$ so it must be easier than that. Suggestions on an article or the property?

Answer 1

The vectors which $Ax=0$ are in the null space of $A$. The null space of $A$ is spanned by the right singular vectors corresponding to zero singular values.