b+ a 3 3b+3 3a 3 b+2 2a + 1 2 2b-5 -5a-7 2 1 b+2 2a +2 Thse vectors can't possibly be linearly independent. Tell why. Next obtain a linearly independent subset of these vectors which has the same span as these vectors. In other words, find a basis for the span of these vectors.
b+ a 3 3b+3 3a 3 b+2 2a + 1 2 2b-5 -5a-7 2 1 b+2 2a +2 Thse vectors can't possibly be linearly independent. Tell why. Next obtain a linearly independent subset of these vectors which has the same span as these vectors. In other words, find a basis for the span of these vectors.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![The vectors given are:
\[
\begin{bmatrix}
1 \\
b + 1 \\
a \\
1
\end{bmatrix}, \quad
\begin{bmatrix}
3 \\
3b + 3 \\
3a \\
3
\end{bmatrix}, \quad
\begin{bmatrix}
1 \\
b + 2 \\
2a + 1 \\
1
\end{bmatrix}, \quad
\begin{bmatrix}
2 \\
2b - 5 \\
-5a - 7 \\
2
\end{bmatrix}, \quad
\begin{bmatrix}
1 \\
b + 2 \\
2a + 2 \\
1
\end{bmatrix}
\]
These vectors can’t possibly be linearly independent. Tell why. Next obtain a linearly independent subset of these vectors which has the same span as these vectors. In other words, find a basis for the span of these vectors.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc8f5e3d6-55b9-49b4-b3a6-fa76eb7ebbe0%2F1122b405-2b9b-4625-86bf-22a75cd4949f%2Fkg7fwlh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The vectors given are:
\[
\begin{bmatrix}
1 \\
b + 1 \\
a \\
1
\end{bmatrix}, \quad
\begin{bmatrix}
3 \\
3b + 3 \\
3a \\
3
\end{bmatrix}, \quad
\begin{bmatrix}
1 \\
b + 2 \\
2a + 1 \\
1
\end{bmatrix}, \quad
\begin{bmatrix}
2 \\
2b - 5 \\
-5a - 7 \\
2
\end{bmatrix}, \quad
\begin{bmatrix}
1 \\
b + 2 \\
2a + 2 \\
1
\end{bmatrix}
\]
These vectors can’t possibly be linearly independent. Tell why. Next obtain a linearly independent subset of these vectors which has the same span as these vectors. In other words, find a basis for the span of these vectors.
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