SVD of a matrix

Question

Can someone please tell me the Singular Value Decomposition of A= $\begin{bmatrix} 1 & 0\\ 1 & 0\\ \end{bmatrix} $. I calculated U= $$\begin{bmatrix} \frac{1}{\sqrt2} & \frac{1}{\sqrt2}\\ \frac{-1}{\sqrt2} & \frac{1}{\sqrt2}\\ \end{bmatrix} $$ and the eigenvalues came out to be 0,2. Now I am facing problem with finding V. Can somebody please help me in finding the v1, v2 for V ?

Answer 1

The solution of $A=UDV$ is $$ \left(\begin{matrix}1&0\\1&0\end{matrix}\right)=\left(\begin{matrix}\frac{1}{\sqrt{2}}&-\frac{1}{\sqrt{2}}\\-\frac{1}{\sqrt{2}}&-\frac{1}{\sqrt{2}}\end{matrix}\right)\left(\begin{matrix}0&0\\0&\sqrt{2}\end{matrix}\right) \left(\begin{matrix}0&-1\\-1&0\end{matrix}\right)\,. $$