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V = R' = {(x.y)|x, y e R}, with standard operation of addition on R² which is (x,.y,)+(x,, y2) = (x1 + x,, V1 + Y2) and standard operation of multiplication by scalar which is c(x, y) = (cx,cy).

V = R' = {(x.y)|x, y e R}, with standard operation of addition on R² which is (x,.y,)+(x,, y2) = (x1 + x,, V1 + Y2) and standard operation of multiplication by scalar which is c(x, y) = (cx,cy).

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.1: Inner Product Spaces
Problem 12EQ
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Proof that it is a vector space. Please explain details why it happened with a clear steps. Thank you

V = R' = {(x.y)|x, y e R}, with standard operation of addition on R² which is (x,.y,)+(x,, y2) = (x1 + x,, V1 + Y2) and standard operation of multiplication by scalar which is c(x, y) = (cx,cy).
Transcribed Image Text:V = R' = {(x.y)|x, y e R}, with standard operation of addition on R² which is (x,.y,)+(x,, y2) = (x1 + x,, V1 + Y2) and standard operation of multiplication by scalar which is c(x, y) = (cx,cy).
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