Determine which sets in Exercises 1-8 are bases for R3. Of the sets that are not bases, determine which ones are linearly independent and which ones span R³. Justify your answers.
Determine which sets in Exercises 1-8 are bases for R3. Of the sets that are not bases, determine which ones are linearly independent and which ones span R³. Justify your answers.
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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![The image shows three column vectors for an educational exercise:
1. First vector:
\[
\begin{bmatrix}
1 \\
0 \\
1
\end{bmatrix}
\]
2. Second vector:
\[
\begin{bmatrix}
0 \\
0 \\
0
\end{bmatrix}
\]
3. Third vector:
\[
\begin{bmatrix}
0 \\
1 \\
0
\end{bmatrix}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe8fabc15-e5db-480c-94d9-e42b67b656a8%2Fe656ee39-8ed9-4b25-8d72-80930c3aa760%2Fu377jk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image shows three column vectors for an educational exercise:
1. First vector:
\[
\begin{bmatrix}
1 \\
0 \\
1
\end{bmatrix}
\]
2. Second vector:
\[
\begin{bmatrix}
0 \\
0 \\
0
\end{bmatrix}
\]
3. Third vector:
\[
\begin{bmatrix}
0 \\
1 \\
0
\end{bmatrix}
\]
Transcribed Image Text:Determine which sets in Exercises 1–8 are bases for \( \mathbb{R}^3 \). Of the sets that are not bases, determine which ones are linearly independent and which ones span \( \mathbb{R}^3 \). Justify your answers.
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