Exercise 9.1.2 Consider R2 with the following non-standard addition operation : (a,b) (c,d) = (0,b+d). Scalar multiplication is defined in the usual way. Is this a vector space? Explain why or why not.
Exercise 9.1.2 Consider R2 with the following non-standard addition operation : (a,b) (c,d) = (0,b+d). Scalar multiplication is defined in the usual way. Is this a vector space? Explain why or why not.
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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Can you help me solve question 9.1.2 and please why or why not please
![**Exercise 9.1.2** Consider \(\mathbb{R}^2\) with the following non-standard addition operation \(\oplus\):
\[
(a, b) \oplus (c, d) = (0, b + d).
\]
Scalar multiplication is defined in the usual way. Is this a vector space? Explain why or why not.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F52fb4760-8b56-41d1-811f-26cd2f9d5b41%2F26f03a49-3bc2-4475-acf0-90df91f0504a%2Fpypk72k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Exercise 9.1.2** Consider \(\mathbb{R}^2\) with the following non-standard addition operation \(\oplus\):
\[
(a, b) \oplus (c, d) = (0, b + d).
\]
Scalar multiplication is defined in the usual way. Is this a vector space? Explain why or why not.
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