Exercise 9.1.1 Consider the set R² with the following non-standard addition operation : (a,b) (c,d) = (a +d,b+c). Scalar multiplication is defined in the usual way. Is this a vector space? Explain why or why not.
Exercise 9.1.1 Consider the set R² with the following non-standard addition operation : (a,b) (c,d) = (a +d,b+c). Scalar multiplication is defined in the usual way. Is this a vector space? Explain why or why not.
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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![**Exercise 9.1.1**
Consider the set \(\mathbb{R}^2\) with the following non-standard addition operation \(\oplus\):
\[
(a, b) \oplus (c, d) = (a + d, b + c).
\]
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%2F5dabe4e8-4d41-42d6-aeb9-4a7fca8c4b16%2F4044c4a4-27b0-4264-bbc4-224d3c870b80%2Fai8fwu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Exercise 9.1.1**
Consider the set \(\mathbb{R}^2\) with the following non-standard addition operation \(\oplus\):
\[
(a, b) \oplus (c, d) = (a + d, b + c).
\]
Scalar multiplication is defined in the usual way. Is this a vector space? Explain why or why not.
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