Please show your work

6. (20 pts) Let A = KNOL and b (a) (5 pts) Select the correct statement and explain your reasoning (select one). i. Since rank(A) = 1, we know there is no solution to the normal equations for Ax = b. ii. Since rank(A) = 1, we know there is a unique solution to the normal equa- tions for Ax = b. iii. Since rank(A) = 1, we know there are many solutions to the normal equa- tions for Ax = b. iv. Since rank(A) = 2, we know there is no solution to the normal equations for Ax = b. V. Since rank(A) = 2, we know there is a unique solution to the normal equa- tions for Ax = b. vi. Since rank(A) = 2, we know there are many solutions to the normal equa- tions for Ax = b. vii. Since rank(A) = 4, we know there is no solution to the normal equations for Ax = b. viii. Since rank(A) = 4, we know there is a unique solution to the normal equa- tions for Ax = b. ix. Since rank(A) = 4, we know there are many solutions to the normal equa- tions for Ax = b. Problem continues on next page.(b) (10 pts) Find the least squares solution(s) for the system Ax = b. Do not a use a computer, show all your work. (c) (5 pts) Select the best word to fill in the blank, and explain your reasoning: The least squares solution for Ax = b can be used to construct the. function whose graph comes closest to passing through all the points (-1, -1), (0, 1), (2, 2) and (-2, 1). (Select one) i. constant ii. linear iii. quadratic iv. cubic