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d. a specific element of R° that is not in V. е. a specific element of v in V for which -v is not in V.

d. a specific element of R° that is not in V. е. a specific element of v in V for which -v is not in V.

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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i need help with d and e

Consider the set V of all real triples of the form \((a, b, c)\) where \(c = a - 2b\) under the usual vector addition and scalar multiplication of \(\mathbb{R}^3\). This same candidate for a Vector Space (or Subspace of \(\mathbb{R}^3\)) is used in the next question. Give the following (fill in the blanks) examples of 3-tuples in V as requested. **Write your answers as comma-delimited triples using parentheses. For ease in reading, place a space after each comma. If no such requested element exists, write the word "none" in the box (no quotation marks).** a. a specific element of V whose first and third components are the same: \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\) b. a specific element of V whose third component is 6. \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\) c. a non-zero specific element of V whose second component is -1. \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\) d. a specific element of \(\mathbb{R}^3\) that is not in V. \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\) e. a specific element of V in V for which \(-v\) is not in V. \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\)
Transcribed Image Text:Consider the set V of all real triples of the form \((a, b, c)\) where \(c = a - 2b\) under the usual vector addition and scalar multiplication of \(\mathbb{R}^3\). This same candidate for a Vector Space (or Subspace of \(\mathbb{R}^3\)) is used in the next question. Give the following (fill in the blanks) examples of 3-tuples in V as requested. **Write your answers as comma-delimited triples using parentheses. For ease in reading, place a space after each comma. If no such requested element exists, write the word "none" in the box (no quotation marks).** a. a specific element of V whose first and third components are the same: \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\) b. a specific element of V whose third component is 6. \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\) c. a non-zero specific element of V whose second component is -1. \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\) d. a specific element of \(\mathbb{R}^3\) that is not in V. \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\) e. a specific element of V in V for which \(-v\) is not in V. \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\)
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