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7. Let V={(x,y) x,y € R}. Suppose addition and scalar multiplication are defined using the following non-standard rules where c is any real number. (x,y)+(x₂.₂)-(x₂-x₂.0) c(x,y)=(-x,,Scy,) a. Find the result of (3,-2) + (-4,-3) under the above operations. b. Find the result of -3(2,-4) under the above operations. c. Show that V, with respect to these operations of addition and scalar multiplication, is not a vector space by showing that one of the vector space axioms does not hold. Clearly identify the axiom you have chosen.

7. Let V={(x,y) x,y € R}. Suppose addition and scalar multiplication are defined using the following non-standard rules where c is any real number. (x,y)+(x₂.₂)-(x₂-x₂.0) c(x,y)=(-x,,Scy,) a. Find the result of (3,-2) + (-4,-3) under the above operations. b. Find the result of -3(2,-4) under the above operations. c. Show that V, with respect to these operations of addition and scalar multiplication, is not a vector space by showing that one of the vector space axioms does not hold. Clearly identify the axiom you have chosen.

Advanced Engineering Mathematics
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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7. Let V={(x,y) x,y e R}. Suppose addition and scalar multiplication are defined using the following non-standard rules where c is any real number. (x,y) + (x₂,₂)=(x₁-x₂₂0) c(x,y)=(-x,₁,Scy,) a. Find the result of (3,-2) + (-4,-3) under the above operations. b. Find the result of -3(2,-4) under the above operations. c. Show that V, with respect to these operations of addition and scalar multiplication, is not a vector space by showing that one of the vector space axioms does not hold. Clearly identify the axiom you have chosen.
Transcribed Image Text:7. Let V={(x,y) x,y e R}. Suppose addition and scalar multiplication are defined using the following non-standard rules where c is any real number. (x,y) + (x₂,₂)=(x₁-x₂₂0) c(x,y)=(-x,₁,Scy,) a. Find the result of (3,-2) + (-4,-3) under the above operations. b. Find the result of -3(2,-4) under the above operations. c. Show that V, with respect to these operations of addition and scalar multiplication, is not a vector space by showing that one of the vector space axioms does not hold. Clearly identify the axiom you have chosen.
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