Let V be the set of all pairs (x,y) of real numbers together with the following operations: (x1,y1)(x2,y2) = (x1 + x2 − 2, y1 + y2) - c(x,y) = (cx-2c+2, cy - 5c+5). (a) Show that 1 is a scalar multiplication identity, that is: 10(x,y) = (x,y). (b) Explain why V nonetheless is not a vector space. Hint: Check for if scalar multiplication distributes over vector addition.

Let V be the set of all pairs (x,y) of real numbers together with the following operations: (x1,y1)(x2,y2) = (x1 + x2 − 2, y1 + y2) - c(x,y) = (cx-2c+2, cy - 5c+5). (a) Show that 1 is a scalar multiplication identity, that is: 10(x,y) = (x,y). (b) Explain why V nonetheless is not a vector space. Hint: Check for if scalar multiplication distributes over vector addition.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.1: Real Numbers

Problem 40E

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