(a) Determine the adjoint operator, A*(Y]. (b) Derive the normal equations (i.e., the algebraic condition that a least squares solution, X , must satisfy) and the algebraic condition for a solution, X , to be minimum norm. (c) For the operator A ltol derive a closedform expression for the solution and for the pseudoin verse, A+(Y). Justify every key step in your derivation (d) For A ltol give a closedform expression for the orthogonal projector onto R{A]. (e) for A onto derive a closedform expression for the solution and for the pseudoinverse, A+{Y). Justify every key step in your solution. ( For A onto give a closedform expression for the orthogonal projector onto RLA")