Let $A,b$ be as defined below. Use the SVD to write $b=$hat$(b)+z,$ where hat$(b)inCol(A)$ and zin

$ull(A^T).$

$A=\left[\begin{array}{cc}1& 2\\ 3& 4\\ 1& 1\\ 1& -1\end{array}\right],b=\left[\begin{array}{c}1\\ 2\\ 3\\ 4\end{array}\right]$

Also write in Python how you would check to see if hat$(b)$ is actually in the column space of $A($using the output

of the SVD$).$