3. For each set below, circie YES' it it is a vector space, or circle "NO" if it is not a vectorspace. Whenever you circle "YES" you do not have to justify your answer. Wheneveryou circle "NO", give a counterexample/reason.-S = {a + bx + cx² e P2: abc = 0}a.YESNOCounterexample:A lo 3aC 0Le f 0.deM3: a, b, c, d, e,feb. A =YESNOCounterexample:A 1oC. Let the vector space V be the set of real numbers, with addition and scalarmultiplication defined byx+y= the maximum of x and ykx = kx (the usual scalar multiplication of R)YESNOCounterexample:

First and last one has counter examples see the step 2 and second one is true

3. For each set below, circle "YES" it it is a vector space, or circle "NO" if it is not a vector space. Whenever you circle "YES" you do not have to justify your answer. Whenever you circle "NO", give a counterexample/reason.- S = {a + bx + cx² e P2: abc = 0} a. YES NO Counterexample: a C 0 Le f 0. deM3: a, b, c, d, e,fe b. A = YES NO Counterexample: Alo C. Let the vector space V be the set of real numbers, with addition and scalar multiplication defined by x+y= the maximum of x and y kx = kx (the usual scalar multiplication of R) YES NO Counterexample:

3. For each set below, circle "YES" it it is a vector space, or circle "NO" if it is not a vector space. Whenever you circle "YES" you do not have to justify your answer. Whenever you circle "NO", give a counterexample/reason.- S = {a + bx + cx² e P2: abc = 0} a. YES NO Counterexample: a C 0 Le f 0. deM3: a, b, c, d, e,fe b. A = YES NO Counterexample: Alo C. Let the vector space V be the set of real numbers, with addition and scalar multiplication defined by x+y= the maximum of x and y kx = kx (the usual scalar multiplication of R) YES NO Counterexample:

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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