Find a basis for the subspace of R* spanned by S. S = {(5, 9, –5, 53), (-3, 5, 3, -5), (8, –3, –8, 17), (0, –3, 0, 15)}
Find a basis for the subspace of R* spanned by S. S = {(5, 9, –5, 53), (-3, 5, 3, -5), (8, –3, –8, 17), (0, –3, 0, 15)}
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
100%
4.6
5.
pls help
![**Find a basis for the subspace of \( \mathbb{R}^4 \) spanned by \( S \).**
\[ S = \{(5, 9, -5, 53), (-3, 5, 3, -5), (8, -3, -8, 17), (0, -3, 0, 15)\} \]
### Visual Explanation:
The image shows a matrix concept where each provided vector from set \( S \) is to be considered as either rows or columns of a matrix. The goal is to determine the basis for the span of these vectors.
1. **Matrix Representation (Not explicitly shown):**
- The vectors are transformed into a matrix format, where each vector could potentially be a row in the matrix.
- The empty boxes suggest places where elements of \( S \) will be fitted either as columns or rows.
2. **Arrow Indicators:**
- **Downward Arrows:** These imply operations that might involve row reduction or selecting linearly independent rows/columns.
- **Rightward Arrows:** Indicate the transformation or shift where parts of the matrix are considered in determining independence, possibly involving Gaussian elimination or pivoting.
3. **Objective:**
- The objective is to manipulate these vectors/matrix to find the linearly independent set that serves as a basis for the subspace spanned by \( S \). This involves identifying vectors that provide the maximum independent span without redundancy.
This type of vector analysis is typically solved by forming the associated matrix from \( S \) and performing row reduction (Gaussian elimination) to achieve row-echelon form. The non-zero rows act as a basis for the subspace in \( \mathbb{R}^4 \) spanned by the set \( S \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc42b80bf-a5d4-414b-bce1-0fe52a04dbbd%2Fa8bc98d6-5afb-45ec-b866-370f7886ea14%2Fufbtcaw_processed.png&w=3840&q=75)
Transcribed Image Text:**Find a basis for the subspace of \( \mathbb{R}^4 \) spanned by \( S \).**
\[ S = \{(5, 9, -5, 53), (-3, 5, 3, -5), (8, -3, -8, 17), (0, -3, 0, 15)\} \]
### Visual Explanation:
The image shows a matrix concept where each provided vector from set \( S \) is to be considered as either rows or columns of a matrix. The goal is to determine the basis for the span of these vectors.
1. **Matrix Representation (Not explicitly shown):**
- The vectors are transformed into a matrix format, where each vector could potentially be a row in the matrix.
- The empty boxes suggest places where elements of \( S \) will be fitted either as columns or rows.
2. **Arrow Indicators:**
- **Downward Arrows:** These imply operations that might involve row reduction or selecting linearly independent rows/columns.
- **Rightward Arrows:** Indicate the transformation or shift where parts of the matrix are considered in determining independence, possibly involving Gaussian elimination or pivoting.
3. **Objective:**
- The objective is to manipulate these vectors/matrix to find the linearly independent set that serves as a basis for the subspace spanned by \( S \). This involves identifying vectors that provide the maximum independent span without redundancy.
This type of vector analysis is typically solved by forming the associated matrix from \( S \) and performing row reduction (Gaussian elimination) to achieve row-echelon form. The non-zero rows act as a basis for the subspace in \( \mathbb{R}^4 \) spanned by the set \( S \).
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 1 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,
