Problem 6. Define new addition and scalar multiplication operations and on R² by (x, y) + (z, w) = (x+z, y+w), (x, y) = (ax, y), a for all (x, y), (z, w) € R² and a € R. Does R² with these operations form a vector space over R? Justify your answer.
Problem 6. Define new addition and scalar multiplication operations and on R² by (x, y) + (z, w) = (x+z, y+w), (x, y) = (ax, y), a for all (x, y), (z, w) € R² and a € R. Does R² with these operations form a vector space over R? Justify your answer.
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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Transcribed Image Text:Problem 6. Define new addition and scalar multiplication operations and on R² by
(x, y) + (z, w) = (x+z, y+w),
a (x, y) = (ax, y),
for all (x, y), (z, w) € R² and a € R. Does R² with these operations form a vector
space over R? Justify your answer.
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