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If A = 1-3 -1 1 0 -1 1 1 is v = 5 in null(A)? O v is in null(A). Ov is not in null(A).

If A = 1-3 -1 1 0 -1 1 1 is v = 5 in null(A)? O v is in null(A). Ov is not in null(A).

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Linear Algebra: Checking if a Vector is in the Null Space **Problem Statement:** Given the matrix \( A \) and vector \( \mathbf{v} \), determine if \( \mathbf{v} \) is in the null space of \( A \). Matrix \( A \) is defined as: \[ A = \begin{bmatrix} 1 & 0 & -1 \\ 1 & 1 & 1 \end{bmatrix} \] Vector \( \mathbf{v} \) is: \[ \mathbf{v} = \begin{bmatrix} -1 \\ 5 \\ -1 \end{bmatrix} \] **Question:** Is \( \mathbf{v} \) in \( \text{null}(A) \)? - ☐ \( \mathbf{v} \) is in \( \text{null}(A) \). - ☐ \( \mathbf{v} \) is not in \( \text{null}(A) \). **Explanation:** To determine if \( \mathbf{v} \) is in \( \text{null}(A) \), compute \( A \mathbf{v} \). If the result is the zero vector, \( \mathbf{v} \) is in the null space of \( A \). Otherwise, it is not.
Transcribed Image Text:### Linear Algebra: Checking if a Vector is in the Null Space **Problem Statement:** Given the matrix \( A \) and vector \( \mathbf{v} \), determine if \( \mathbf{v} \) is in the null space of \( A \). Matrix \( A \) is defined as: \[ A = \begin{bmatrix} 1 & 0 & -1 \\ 1 & 1 & 1 \end{bmatrix} \] Vector \( \mathbf{v} \) is: \[ \mathbf{v} = \begin{bmatrix} -1 \\ 5 \\ -1 \end{bmatrix} \] **Question:** Is \( \mathbf{v} \) in \( \text{null}(A) \)? - ☐ \( \mathbf{v} \) is in \( \text{null}(A) \). - ☐ \( \mathbf{v} \) is not in \( \text{null}(A) \). **Explanation:** To determine if \( \mathbf{v} \) is in \( \text{null}(A) \), compute \( A \mathbf{v} \). If the result is the zero vector, \( \mathbf{v} \) is in the null space of \( A \). Otherwise, it is not.
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