Show that the set of all pairs of real numbers (x, y) with the operations(X1, Y1) + (x2, Y2) = (x1 + x2 + 1, y1 + Y2+ 1) andk (*1, Y1) = (kx1, kyı)is not a vector space.

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Answered: Show that the set of all pairs of real…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.3: Spanning Sets And Linear Independence

Problem 45EQ

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Show that the set of all pairs of real numbers (x, y) with the operations (X1, Y1) + (x2, Y2) = (x1 + x2 + 1, y1 + Y2+ 1) and k (*1, Y1) = (kx1, kyı) is not a vector space.