Question: Let A Rmx be a matrix such that its row are linearly independent (as vectors in R) and let b E R. such that

Let A Rmx be a matrix such that its row are linearly independent (as vectors in R") and let b E R. such that the set H = {x R": Ax=b} Is nonempty. 1) Prove that H is a closed and convex subset of R". 2) Let a ER". By considering the optimization problem (7) (min|lx-al| s. t. Ax = b and using the KKT theorem, prove that P(a) = a + A (AA)-(b - Aa).

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