1 Determine whether the set 1 1 is a basis for R3. If the set is not a basis, determine whether the set is linearly independent and whether the set spans R3. Which of the following describe the set? Select all that apply. A. The set spans Rº. B. The set is a basis for R Click to select your answer(s).

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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1
Determine whether the set
1
1
is a basis for R3. If the set is not a basis, determine whether the set is linearly independent and whether the set
spans R3.
Which of the following describe the set? Select all that apply.
A. The set spans Rº.
B. The set is a basis for R
Click to select your answer(s).
Transcribed Image Text:1 Determine whether the set 1 1 is a basis for R3. If the set is not a basis, determine whether the set is linearly independent and whether the set spans R3. Which of the following describe the set? Select all that apply. A. The set spans Rº. B. The set is a basis for R Click to select your answer(s).
Expert Solution
Step 1

Given  the set S=010,110,000, we need to check whether S is a basis and if it is not a basis we need to check whether it is linearly independent and whether it spans 3.

Solution:

Lets check whether the set S is linearly independent.

The set S=010,110,000 has a 000 vector, therefore it is linearly dependent as 1000=0010+0110 that is  the non-trivial linear combination is equal to 0.

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