Please provide steps, Thank you.

1) Projection to a set of linear constraints: Consider the optimization problem . 1 2 36111;}! illaXII2 (1) st. Ax = b, which projects the point a to the set X {x E R\" s.t. Ax = b}. Suppose that A is a fat matrix and AAT is invertible. - Write down the Lagrangian function. - Find the dual problem of (l). - Write down the KKT conditions for (1). - Let [a]+ be the optimizer of (1). Using KKT conditions and the dual optimization problem, express [a]+ as a function of A, b, a