Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
T F If A is m x n matrix, then ker(A) = ker(AT A).

T F If A is m x n matrix, then ker(A) = ker(AT A).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
### True/False Question: (iii) **T** **F** \_\_\_. If \( A \) is an \( m \times n \) matrix, then \( \text{ker}(A) = \text{ker}(A^T A) \). **Explanation:** This question provides a statement about the relationship between a matrix \( A \) and its transpose multiplied by itself, specifically focusing on their kernels (null spaces). The question asks if the kernel (null space) of \( A \) is equal to the kernel of \( A^T A \), where \( A^T \) represents the transpose of the matrix \( A \). ### Understanding Kernels: - **Kernel of \( A \):** The set of all vectors \( \mathbf{x} \) such that \( A \mathbf{x} = \mathbf{0} \). - **Kernel of \( A^T A \):** The set of all vectors \( \mathbf{x} \) such that \( A^T A \mathbf{x} = \mathbf{0} \). The answer to the question depends on your understanding of linear algebra, specifically the properties of matrices and their kernels.
Transcribed Image Text:### True/False Question: (iii) **T** **F** \_\_\_. If \( A \) is an \( m \times n \) matrix, then \( \text{ker}(A) = \text{ker}(A^T A) \). **Explanation:** This question provides a statement about the relationship between a matrix \( A \) and its transpose multiplied by itself, specifically focusing on their kernels (null spaces). The question asks if the kernel (null space) of \( A \) is equal to the kernel of \( A^T A \), where \( A^T \) represents the transpose of the matrix \( A \). ### Understanding Kernels: - **Kernel of \( A \):** The set of all vectors \( \mathbf{x} \) such that \( A \mathbf{x} = \mathbf{0} \). - **Kernel of \( A^T A \):** The set of all vectors \( \mathbf{x} \) such that \( A^T A \mathbf{x} = \mathbf{0} \). The answer to the question depends on your understanding of linear algebra, specifically the properties of matrices and their kernels.
1. Determine whether each statement is true or false, and justify your answer.
Transcribed Image Text:1. Determine whether each statement is true or false, and justify your answer.
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
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…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS