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) Only S2 and S4 are vector subspaces. (b) The sets S1,S2,S3, and S4 are vector subspaces

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) Only S2 and S4 are vector subspaces. (b) The sets S1,S2,S3, and S4 are vector subspaces

Intermediate Algebra

19th Edition

ISBN:9780998625720

Author:Lynn Marecek

Publisher:Lynn Marecek

Chapter4: Systems Of Linear Equations

Section4.6: Solve Systems Of Equations Using Determinants

Problem 279E: Explain the steps for solving a system of equations using Cramer’s rule.

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Question

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) Only S₂ and S₄ are vector subspaces.

(b) The sets S₁,S₂,S₃, and S₄ are vector subspaces.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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