Given the set V = R over the set of real numbers Q, together with addition and scalar multiplication. Which one of thefollowing subsets of R does not constitute a vector space over Q?A. The set {(0,6):b€ Q}B. The set {(a,0) : a € Q}C. The set {(a, b) : a, b e Z}D. The set {(2a, 2b) : a, b e Q} Given two subspaces A = {(a, b,0) : a,b e R} and B = {(c, 0, d) : c,d e R} of R°.O A. R' is equal to the direct sum A BB. R is equal to the direct sum A O B only if c = 0%3DO C.R' is equal to the direct sum A O B if either a =0 or c = 0D. None of the listed alternatives are true.E. R' is equal to the direct sum A B only if a = 0 and c = 0

Answered: Image /qna-images/answer/c724f89e-fe26-4b7d-a366-c3039e3fed7a.jpg

Given two subspaces A = {(a,b,0): a,b e R} and B = {(c,0, d) : c,d e R} of R°. |3| O A. R' is equal to the direct sum A B O B. R is equal to the direct sum A Bonly if c = 0 O C. R is equal to the direct sum A O B if either a = O or c = 0 O D. None of the listed alternatives are true. O E. R is equal to the direct sum A B only if a O and c = 0

Given two subspaces A = {(a,b,0): a,b e R} and B = {(c,0, d) : c,d e R} of R°. |3| O A. R' is equal to the direct sum A B O B. R is equal to the direct sum A Bonly if c = 0 O C. R is equal to the direct sum A O B if either a = O or c = 0 O D. None of the listed alternatives are true. O E. R is equal to the direct sum A B only if a O and c = 0

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.1: Vector Spaces And Subspaces

Problem 19EQ

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