Question

Let V be the set of vectors shown below. V= [] :x>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. 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 + y must be in V because V is a subset of the vector space R2 O C. 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. OD. The vector u + vis 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. 2 OA. U = C= -1 -2 OB. U= [] c=4 O c. u= -[2] c=4 OD. U= .C= -1 2

Answer 1

Solution het V be the set of vectors, V={[5] aze, 920] a) if u and v are in v then U=w with uczo, U₂20, vizo and 1 7o utvizo . Uz tV270 utve [etri EV U2 1 V₂ oplion c) The vector UFV must be in V, because the x- Coordinate of wer is the sum of two positie numbers which must also be positive and the y-coordenate of utv is the sum of posilue cenabens which must be positie 62 Take u EV and the scalar c= -1 (lev > Cou () ¢v [:-240 option d)