### Null Space of Matrix ALet \[ A = \begin{bmatrix}-1 & 2 & 12 \\0 & 0 & 1 & 10 \\0 & 1 & 0 & -9 \end{bmatrix}.\]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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Answered: -1 1 2 12 Let A 0 1 10 %3D 0 10-9 Find…

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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).

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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Concept explainers

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.

Question

### 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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