In R3, let S be the set of vectors 3 S = {V1, V2, V3, V4} = -3 -2 -4 -4 a. Explain why S spans R³ but is not a basis for R3. b. Delete one of the vectors from S to form a new set of vectors, that is a basis for R3.
In R3, let S be the set of vectors 3 S = {V1, V2, V3, V4} = -3 -2 -4 -4 a. Explain why S spans R³ but is not a basis for R3. b. Delete one of the vectors from S to form a new set of vectors, that is a basis for R3.
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
![In \( \mathbb{R}^3 \), let \( S \) be the set of vectors
\[
S = \{ \mathbf{v_1}, \mathbf{v_2}, \mathbf{v_3}, \mathbf{v_4} \} = \left\{
\begin{bmatrix}
-1 \\
4 \\
-4
\end{bmatrix},
\begin{bmatrix}
1 \\
-3 \\
1
\end{bmatrix},
\begin{bmatrix}
1 \\
-2 \\
0
\end{bmatrix},
\begin{bmatrix}
3 \\
0 \\
-4
\end{bmatrix}
\right\}
\]
a. Explain why \( S \) spans \( \mathbb{R}^3 \) but is not a basis for \( \mathbb{R}^3 \).
b. Delete one of the vectors from \( S \) to form a new set of vectors, that is a basis for \( \mathbb{R}^3 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F690bc708-737a-4036-8bde-cd8ee17ec8dd%2Fb9efd19f-a205-4710-89ef-894ca84f1a19%2Fmyzejkd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In \( \mathbb{R}^3 \), let \( S \) be the set of vectors
\[
S = \{ \mathbf{v_1}, \mathbf{v_2}, \mathbf{v_3}, \mathbf{v_4} \} = \left\{
\begin{bmatrix}
-1 \\
4 \\
-4
\end{bmatrix},
\begin{bmatrix}
1 \\
-3 \\
1
\end{bmatrix},
\begin{bmatrix}
1 \\
-2 \\
0
\end{bmatrix},
\begin{bmatrix}
3 \\
0 \\
-4
\end{bmatrix}
\right\}
\]
a. Explain why \( S \) spans \( \mathbb{R}^3 \) but is not a basis for \( \mathbb{R}^3 \).
b. Delete one of the vectors from \( S \) to form a new set of vectors, that is a basis for \( \mathbb{R}^3 \).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
