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(2) In the following a set V, a field F, which is either R or C (Complex Numbers), and the operations of addition and scalar multiplication are given. Check whether V is a vector space over F, with these operations. (i): With addition and scalar multiplication as in R², (a) V = {(a, b) = R² : 2a + 3b =0}, F = R. (ii): V = R², F = R, with addition as in R2, and scalar multiplication as given by the following: for (a, b) € V, a € R, (a) a(a, b) = (a,0).

(2) In the following a set V, a field F, which is either R or C (Complex Numbers), and the operations of addition and scalar multiplication are given. Check whether V is a vector space over F, with these operations. (i): With addition and scalar multiplication as in R², (a) V = {(a, b) = R² : 2a + 3b =0}, F = R. (ii): V = R², F = R, with addition as in R2, and scalar multiplication as given by the following: for (a, b) € V, a € R, (a) a(a, b) = (a,0).

Advanced Engineering Mathematics
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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(2) In the following a set V, a field F, which is either R or C (Complex Numbers), and the operations of addition and scalar multiplication are given. Check whether V is a vector space over F, with these operations. (i): With addition and scalar multiplication as in R², (a) V = {(a, b) E R² : 2a + 3b = 0}, F = R. (ii): V = R², F =R, with addition as in R?, and scalar multiplication as given by the following: for (a, b) E V, a E R, (a) a(a, b) := (a,0).
Transcribed Image Text:(2) In the following a set V, a field F, which is either R or C (Complex Numbers), and the operations of addition and scalar multiplication are given. Check whether V is a vector space over F, with these operations. (i): With addition and scalar multiplication as in R², (a) V = {(a, b) E R² : 2a + 3b = 0}, F = R. (ii): V = R², F =R, with addition as in R?, and scalar multiplication as given by the following: for (a, b) E V, a E R, (a) a(a, b) := (a,0).
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