0 s 1 0 0 a -b 4. Let A= Ob a , where a, b, c ER and a 70. Suppose rank(A) = 3, and suppose 1 c 0 1 0 V3 11 V3 p 9 the QR-decomposition of A is A = z 0 where p, q, r, s ER 0 V3 No justification is needed on any part of this problem. (a) (6 points) In parts (i) - (iii) below, determine the values of a, b, c that are consistent with the information above and make the given statement true (for some values of the remaining parameters). If there are no such values, write none. (i) (], 2, 3) is a basis of im(A). (ii) q=0. (iii) p= 0 and s = 1. (b) (5 points) Find all values of p, q, r, and s such that ATA= 3 0 V3 0 1 0 30 4 p = 1, and s = 2, find all 0 (c) (5 points) Let E R5. Assuming that QT7 = -2 0 least-squares solutions of the linear system Az = 7 0 s 1 0 0 a -b 4. Let A= Ob a , where a, b, c ER and a 70. Suppose rank(A) = 3, and suppose 1 c 0 1 0 V3 11 V3 p 9 the QR-decomposition of A is A = z 0 where p, q, r, s ER 0 V3 No justification is needed on any part of this problem. (a) (6 points) In parts (i) - (iii) below, determine the values of a, b, c that are consistent with the information above and make the given statement true (for some values of the remaining parameters). If there are no such values, write none. (i) (], 2, 3) is a basis of im(A). (ii) q=0. (iii) p= 0 and s = 1. (b) (5 points) Find all values of p, q, r, and s such that ATA= 3 0 V3 0 1 0 30 4 p = 1, and s = 2, find all 0 (c) (5 points) Let E R5. Assuming that QT7 = -2 0 least-squares solutions of the linear system Az = 7