(Solved): Problem 1. Orthogonal complement. Let U=span110,011 ...

Problem 1. Orthogonal complement. Let $U=\mathrm{span}??\begin{array}{l}1\\ 1\\ 0\end{array}?,?\begin{array}{l}0\\ 1\\ 1\end{array}??$. Find a basis for $U^{+}$. Hint: Choose an arbitrary vector $x\&U$ and we orthogonalization to find $x^1?U$. Problem 2. QR factorization. Let $A?\left[\begin{array}{ll}1& 3\\ 4& 2\end{array}\right].$ Using the orthogonalization procrss, compute a $QR$ factorization of $A$ by hand. Use the Matlab function qr to compute a $QR$ factorization of $A$. Do you get the same factorization in both cases? Problem 3. QR factorization. Let $A??\begin{array}{ll}1& 3\\ 4& 2\\ 3& 3\end{array}?,b??\begin{array}{c}10\\ 0\\ 6\end{array}?.$ Does a solution exist to the equation $Ax=b$ ? Use the Matlab function qr to compute a $QR$ factorization of $A$. If the solution exists, using the $QR$ factors and back substitution, compute a solution of the equation $Ax=b$