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Let V = P2 be the vector space of all polynomials of degree at most 2, with the usual definitions of addition and scalar multiplication, and define W C V by W = {ao + ajx + a2x² : ao, a1, a2 E R with a¡a2 > 0} Which one of the following statements is true? O a. W is closed under addition, but not under scalar multiplication. O b. W is closed under scalar multiplication, but not under addition. W is not closed under either addition or scalar multiplication. O d. W is a subspace of V.

Let V = P2 be the vector space of all polynomials of degree at most 2, with the usual definitions of addition and scalar multiplication, and define W C V by W = {ao + ajx + a2x² : ao, a1, a2 E R with a¡a2 > 0} Which one of the following statements is true? O a. W is closed under addition, but not under scalar multiplication. O b. W is closed under scalar multiplication, but not under addition. W is not closed under either addition or scalar multiplication. O d. W is a subspace of V.

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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Let V = P2 be the vector space of all polynomials of degree at most 2, with the usual definitions of addition and scalar multiplication, and define W CV by W = {ao + ajx + azx² : ao, a1, a2 E R with a1a2 > 0} Which one of the following statements is true? O a. W is closed under addition, but not under scalar multiplication. O b. W is closed under scalar multiplication, but not under addition. O c. W is not closed under either addition or scalar multiplication. O d. W is a subspace of V.
Transcribed Image Text:Let V = P2 be the vector space of all polynomials of degree at most 2, with the usual definitions of addition and scalar multiplication, and define W CV by W = {ao + ajx + azx² : ao, a1, a2 E R with a1a2 > 0} Which one of the following statements is true? O a. W is closed under addition, but not under scalar multiplication. O b. W is closed under scalar multiplication, but not under addition. O c. W is not closed under either addition or scalar multiplication. O d. W is a subspace of V.
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