Let V = {(z, y)|r, y € R} with addition and scalar multiplication defined as u + v = (u + v, - 3, uz + v2 + 1) and ku = (ku,, kuz). respectively, where k is a scalar and u = (u1, u2) and v = (v1, v2). Which of the following is true? O A. The zero of V is (0,0) and lu u. O B. The zero vector in V is (3, -1) and the negative of (2, 7) is (4,9) OCVis a vector space and the zero of V Is (3,-1). O D. 4|(1, 2) + (3, -4) = 4(1,2) + 4(3, -4) and addition is associative. E. The negative of (1, 2) is (-1, -2) and k(lu) = (kl)u for all u e V and all scalars k, 1.
Let V = {(z, y)|r, y € R} with addition and scalar multiplication defined as u + v = (u + v, - 3, uz + v2 + 1) and ku = (ku,, kuz). respectively, where k is a scalar and u = (u1, u2) and v = (v1, v2). Which of the following is true? O A. The zero of V is (0,0) and lu u. O B. The zero vector in V is (3, -1) and the negative of (2, 7) is (4,9) OCVis a vector space and the zero of V Is (3,-1). O D. 4|(1, 2) + (3, -4) = 4(1,2) + 4(3, -4) and addition is associative. E. The negative of (1, 2) is (-1, -2) and k(lu) = (kl)u for all u e V and all scalars k, 1.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Let V
{(x,y)|x,y E R} with addition and scalar multiplication defined as u + v = (u1 + v1 – 3, u2 + v2 + 1) and ku
(ku1, ku2).
|3|
respectively, where k is a scalar and u =
O A. The zero of V is (0, 0) and lu = u.
(U1, U2) and v =
(v1 , v2). Which of the following is true?
B. The zero vector in V is (3, -1) and the negatíve of (2, 7) is (4, 9)
IS
O C.V is a vector space and the zero of V is (3,-1).
O D. 4[(1, 2) + (3, -4)] = 4(1,2) + 4(3, - 4) and addition is associative.
E. The negative of (1, 2) is (-1, - 2) and k(lu)
(kl)u for all u E V and all scalars k, l.
Reset Selection](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe3e52a32-d1c1-4570-8151-b6af2eaa1a96%2F58853667-64b7-40ea-912f-3c8e9a350c94%2Fcyg1p2p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let V
{(x,y)|x,y E R} with addition and scalar multiplication defined as u + v = (u1 + v1 – 3, u2 + v2 + 1) and ku
(ku1, ku2).
|3|
respectively, where k is a scalar and u =
O A. The zero of V is (0, 0) and lu = u.
(U1, U2) and v =
(v1 , v2). Which of the following is true?
B. The zero vector in V is (3, -1) and the negatíve of (2, 7) is (4, 9)
IS
O C.V is a vector space and the zero of V is (3,-1).
O D. 4[(1, 2) + (3, -4)] = 4(1,2) + 4(3, - 4) and addition is associative.
E. The negative of (1, 2) is (-1, - 2) and k(lu)
(kl)u for all u E V and all scalars k, l.
Reset Selection
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