(a) (3%) The Laplace transform is a linear operation.

(b) (5%) When the equation Ax = b is unsolvable, we may consider the so-called least squares problen to find a set of solutions, having the least squares error, fom solving a normal equation. Suppose that rank(A) =k ＜min(m, n) and let A = BC be a full rank decomposition of A . Use the known matrices B, C, and b to describe the unique projection vector p of b onto R(A) with the least || b-pll2.