Question

Let V be the set of vectors shown below. VE :x>0, a. If u and 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 V, is u + v in V? O A. The vector u + v may or may not be in V depending on the values of x and y. 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 negative numbers, which must also be negative O C. The vector u + v must be in V because V is a subset of the vector space R2 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. u= C=4 2 O B. u= C= -1 OC. U= C=4 OD. u= -=[3 C= -1 Click to select your answer.

Answer 1

Va {[:): »20. yxo af @ If u and a in Up why? are in v, is uto Let u- 21 1- 72 to v belongs ya utus x1 + x2 0] CVS Yetyz Since 1,20, 270 => kitao yiz 20 20 Ye tyz co Pence utu Ev Hence correct option is . The vector utu must be in v because the x-coordinate is the two positive numbers, which must also be positive, and the y-coordinate is the sum of negative numbers, which must also be of utu sum of of utv ☺ Find a (u is not in v. specific vector u in v and a specific scalar e such that 2 པའི ic=4

250 1 Here 4= [3] y coordinate ko € V (1 So u 2 u= B csal 2 Hence U EV 250, -230 z cu=(-1) 12 2 and Lo coordinate yo y Here 2 a coordinate cu & V 2 c 270, -230 c=4 [ 2 ] -2 Hence u EU eu > 414-4 Too a coordinate yo and Here coordinate to y Hence cu EU. is correct option น2 2 ( 2 c=-| 2 y 270 coordinate ko So u&u. Hence correct option is ©