onsider 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 R3. This same candidate for a ector Space (or Subspace of R3) is used in the next question in this exam. ive 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 ace a space after each comma. If no such requested element exists, write the word "none" in the box (no quotation marks). a specific element of V whose first and third components are the same: a specific element of V whose third component is 6. a non-zero specific element of V whose second component is -1.
onsider 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 R3. This same candidate for a ector Space (or Subspace of R3) is used in the next question in this exam. ive 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 ace a space after each comma. If no such requested element exists, write the word "none" in the box (no quotation marks). a specific element of V whose first and third components are the same: a specific element of V whose third component is 6. a non-zero specific element of V whose second component is -1.
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: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 in this exam.
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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