Question

1 0 -7 3 Let A= 03 -4 and b= Denote the columns of A by a, a, ay, and let W = Span{a,,a,,a3} -26 2 3 a. Is b in {a,,a,,az)? How many vectors are in {a,az.az)? b. Is b in W? How many vectors are in W? c. Show that az is in W. (Hint: Row operations are unnecessary.] a. Is b in {a,,a,,az)? Ο Νο Yes How many vectors are in {a,,a,a}? O A. Two OB. Infinitely many OC. Three OD. One b. Set up the appropriate augmented matrix for determining if bis in W. (Simplify your answers.) Is b in W? O A. Yes, because the row-reduced form of the augmented matrix has a pivot in the rightmost column. O B. Yes, because the row-reduced form of the augmented matrix does not have a pivot in the rightmost column. O C. No, because the row-reduced form of the augmented matrix does not have a pivot in the rightmost column. OD. No, because the row-reduced form of the augmented matrix has a pivot in the rightmost column.

Answer 1

o -7 3 0 3 and b = - ] -2 6 2 a (9,822,93) = [:] [:E:] in {a, clearly b is hot 9₂,93} there are three vectors in in {9,92, as} - - 7 = 3 1 (30) - 7(6) O (Al = -2 6 2 -12 #0 cs Scanned Alth 90 CamScanner

is. since TAL #0, so line arly independent spans IR². R3 (a., 92, 93} {a,,42,43} so 3 b = ER3 Hence b is in w. IR3. {aai + Ba₂+ ra, I 14,B, ER} infinitely many rectors so there are in w. © span {a , a2, 93} ני W = {2a, tß a₂, raz 12, B, RER} choosing. 2-0, B =0, r= 1 ca, +ß a2 + raz Ew. 1 oa, to a2 + 193 Ew. a3 EW. Hence az is in w. CS Scanned with CamScanner