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-1 1 2 12 Let A 0 1 10 %3D 0 10-9 Find a nonzero vector u in Nul(A).

-1 1 2 12 Let A 0 1 10 %3D 0 10-9 Find a nonzero vector u in Nul(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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### Null Space of Matrix A Let \[ A = \begin{bmatrix} -1 & 2 & 12 \\ 0 & 0 & 1 & 10 \\ 0 & 1 & 0 & -9 \end{bmatrix}. \] Find a nonzero vector \(\mathbf{u}\) in \(\text{Null}(A)\). \[ \mathbf{u} = \begin{bmatrix} \quad \\ \quad \\ \quad \\ \quad \end{bmatrix} \] In this task, we are given a matrix \( A \) and asked to find a nonzero vector \( \mathbf{u} \) in the null space of \( A \). The null space (or kernel) of a matrix \( A \) is the set of all vectors \( \mathbf{x} \) such that \( A\mathbf{x} = \mathbf{0} \). To find a nonzero vector in the null space, you can set up the augmented matrix [A | 0] and then row reduce it to find the solutions to this homogeneous system. Please fill in the blanks for the null-space vector \( \mathbf{u} \) once the calculations are complete.
Transcribed Image Text:### Null Space of Matrix A Let \[ A = \begin{bmatrix} -1 & 2 & 12 \\ 0 & 0 & 1 & 10 \\ 0 & 1 & 0 & -9 \end{bmatrix}. \] Find a nonzero vector \(\mathbf{u}\) in \(\text{Null}(A)\). \[ \mathbf{u} = \begin{bmatrix} \quad \\ \quad \\ \quad \\ \quad \end{bmatrix} \] In this task, we are given a matrix \( A \) and asked to find a nonzero vector \( \mathbf{u} \) in the null space of \( A \). The null space (or kernel) of a matrix \( A \) is the set of all vectors \( \mathbf{x} \) such that \( A\mathbf{x} = \mathbf{0} \). To find a nonzero vector in the null space, you can set up the augmented matrix [A | 0] and then row reduce it to find the solutions to this homogeneous system. Please fill in the blanks for the null-space vector \( \mathbf{u} \) once the calculations are complete.
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