Let V = R². Show that V is not a real vector space with respect to the following operations of the scalar addition and vector multiplication in V. (x,y) (x,y) = ((x+x)², (y + y)²) c O(x, y) = (cx, cy) (B) Closure Property of Scalar Multiplication (a) Closure Property of Vector Addition It is CLOSED / NOT CLOSED under Vector Addition. It is CLOSED/NOT CLOSED under Scalar Multiplication (a) Commutative Property of Vector Addition (e) Distributive Property of SM over Vector Addition The axiom holds/does not hold. (b) Associative Property of Vector Addition The axiom holds/does not hold. (c) Identity Element of Vector Addition The identity element exists. (d) Additive Inverse The additive inverse exists/ does not exist. The axiom holds/does not hold. (f) Distributive Property of SM over Scalar Addition The axiom holds/does not hold. (g) Distributive Property of SM over SM The axiom holds/does not hold. (h)Identity Element of Scalar Multiplication The axiom holds/does not hold.

Let V = R². Show that V is not a real vector space with respect to the following operations of the scalar addition and vector multiplication in V. (x,y) (x,y) = ((x+x)², (y + y)²) c O(x, y) = (cx, cy) (B) Closure Property of Scalar Multiplication (a) Closure Property of Vector Addition It is CLOSED / NOT CLOSED under Vector Addition. It is CLOSED/NOT CLOSED under Scalar Multiplication (a) Commutative Property of Vector Addition (e) Distributive Property of SM over Vector Addition The axiom holds/does not hold. (b) Associative Property of Vector Addition The axiom holds/does not hold. (c) Identity Element of Vector Addition The identity element exists. (d) Additive Inverse The additive inverse exists/ does not exist. The axiom holds/does not hold. (f) Distributive Property of SM over Scalar Addition The axiom holds/does not hold. (g) Distributive Property of SM over SM The axiom holds/does not hold. (h)Identity Element of Scalar Multiplication The axiom holds/does not hold.

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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