(Solved): Let A=111222120022033 (a) Find the complete solution of Ax=0. (b) Find t ...

Let $$A=\left(\begin{array}{ccccc}1& 2& 1& 0& 0\\ 1& 2& 2& 2& 3\\ ?1& ?2& 0& 2& 3\end{array}\right)$$ (a) Find the complete solution of $$Ax=0$$. (b) Find the complete solution of $$Ax=(1,2,0{)}^T$$. (c) Find the linear condition(s) on $$b_1,b_2,b_3$$ that guarantee that the system $$Ax={\left(b_1,b_2,b_3\right)}^T$$ has a solution. (d) Find the rank of $$A$$ and dimensions of the four subspaces of $$A$$. (e) Find bases of the four fundamental subepaces of $$A$$.