Answered: If scalar multiplication and addition…

If scalar multiplication and addition is redefined on R² in the following way, show that it is NOT a vector space. (x1, Y1) + (x2, Y2) = (x1x2, Y1 Y2) & c(x, y) = (cx,cy)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.2: Vector Spaces

Problem 38E: Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1)...

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

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If scalar multiplication and addition is redefined on R² in the following way, show that it is NOT a vector space.
(x1, Y1) + (x2, Y2) = (x1x2, Y1 Y2) & c(x, y) = (cx,cy)

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