An m × n matrix has full row rank if its row rank is m, and it has full column rank if its column rank is n.
(a) Show that a matrix can have both full row rank and full column rank only if it is square.
(b) Prove that the linear system with matrix of coefficients A has a solution for any d1, . . . , dn's on the right side if and only if A has full row rank.
(c) Prove that a homogeneous system has a unique solution if and only if its matrix of coefficients A has full column rank.
(d) Prove that the statement "if a system with matrix of coefficients A has any solution then it has a unique solution" holds if and only if A has full column rank.