Question

Let V be the set of vectors shown below. V= Ox>0, y>0 a. If u and v are in V, is u + v in V? Why? b. Find a specific vector u in V and a specific scalar c such that cu is not in V. a. If u and v are in Vis u + vin V? O A. The vector u + v must be in V because V is a subset of the vector space R2 OB. The vector u + v must be in V because the x-coordinate of u + v is the sum of two positive numbers, which must also be positive, and the y-coordinate of u + v is the sum of positive numbers, which must also be positive. OC. The vector u + v may or may not be in V depending on the values of x and y. OD. The vector u + v is never in V because the entries of the vectors in V are scalars and not sums of scalars. b. Find a specific vector u in V and a specific scalar c such that cu is not in V. Choose the correct answer below. O A. = C= 4 OB. u= li -] -[] .C= -1 -2 O C. u= c= -1 OD. u= -2.c c=4

Answer 1

V= ca) Let u = and v= y) utv Given {C): x>0, 980} x,>0, y²0 v-[:] : %)0, 4:30 then CI+(*)-(*): X , ,X2,4₂,42 so pcs +xz>o , EY, tY₂)>0 sum of twee of two positive neember posiilive. JEU must be in v because the x-coordinate of is sum of two positive neembors, which must also be positive, and y-cordinate of utv is sum of positive numbers, which meest positive . because is xs+22 4, +42 B. The vector utv utv also be (6) find U EV and scolar c such that cu &u here u= : 200,200 J CEV and scolar c= -1 then cu (J (3) - [3) bul -2 *°, -230 [13] -1 cu&u. T c. u= (=-). Ang