(1) Let A be an m × n matrix and b be an m x 1 matrix. Let Ax =+ b be a consistent linear system of m equations in

n unknowns. In part (ii),determine only if the statement is true or false; do not justify your answer. (i) (4 points) Let N(A) and R(A) stand for the null space and range(i.e., image) of A, respectively. (a) Let P be the solution set for the system (*). For which b do we have P = N(A)? (b) Give a set-notation definition of R(A) (i.e., R(A) = {....}) in terms of column vectors a¡,...,an of A. (ii) (2 points) T/F: The system (*) has at least one free variable if and only if (*) has infinitely many solutions. (iii) (4 points)Prove that if (*) has exactly one solution, then m >= n. (iv) (4 points) Let (*) have infinitely many solutions. Prove that there is no m x 1 matrix c such that the system Ax =+ c has a unique solution.