About the sets, S1 = {(x,y) ∈ R2: x = y3} S2 = {(x,y,z) ∈ R3: x = (y−z)2} S3 = {(x,y) ∈ R2: x4 + y4=0} S4 = {f(x) ∈ P3(R): f(0) = f(1)} Bearing in mind that P3(R) is the set of polynomials of degree at most 3, with coefficients in R, judge as true or false: (a) S4 is a subspace of P3(R). (b) S3 is a subspace of R2.
About the sets, S1 = {(x,y) ∈ R2: x = y3} S2 = {(x,y,z) ∈ R3: x = (y−z)2} S3 = {(x,y) ∈ R2: x4 + y4=0} S4 = {f(x) ∈ P3(R): f(0) = f(1)} Bearing in mind that P3(R) is the set of polynomials of degree at most 3, with coefficients in R, judge as true or false: (a) S4 is a subspace of P3(R). (b) S3 is a subspace of R2.
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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About the sets,
S1 = {(x,y) ∈ R2: x = y3}
S2 = {(x,y,z) ∈ R3: x = (y−z)2}
S3 = {(x,y) ∈ R2: x4 + y4=0}
S4 = {f(x) ∈ P3(R): f(0) = f(1)}
Bearing in mind that P3(R) is the set of polynomials of degree at most 3, with coefficients in R, judge as true or false:
(a) S4 is a subspace of P3(R).
(b) S3 is a subspace of R2.
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