d an explicit description of the null space of matrix A by listing vectors that span the null space. 1-2 3-3-1 1) A-2 5-5 4 1 -1 3-2 1 0 A) C) 0 1 5 1 -7 -2 -3 -1 1 7 -2 0 1 0 16V (CB) D) N 1 0 1 -1 2 0 8888 -1 1 0 m 2 0 1 0 1 0
d an explicit description of the null space of matrix A by listing vectors that span the null space. 1-2 3-3-1 1) A-2 5-5 4 1 -1 3-2 1 0 A) C) 0 1 5 1 -7 -2 -3 -1 1 7 -2 0 1 0 16V (CB) D) N 1 0 1 -1 2 0 8888 -1 1 0 m 2 0 1 0 1 0
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
![**Topic**: Finding the Null Space of a Matrix
To find an explicit description of the null space of a matrix \( A \), one must identify the vectors that span the null space.
**1) Given Matrix:**
\[
A = \begin{bmatrix}
1 & -2 & 3 & -3 & -1 \\
-2 & 5 & -5 & 4 & 1 \\
-1 & 3 & -2 & 1 & 0
\end{bmatrix}
\]
- **Options for Null Space Vectors:**
A)
\[
\begin{bmatrix}
1 \\ 0 \\ 5 \\ -7 \\ -3
\end{bmatrix}
\quad
\begin{bmatrix}
0 \\ 1 \\ -2 \\ -1 \\ -1
\end{bmatrix}
\]
B)
\[
\begin{bmatrix}
2 \\ 1 \\ 0 \\ 0 \\ 0
\end{bmatrix}
\quad
\begin{bmatrix}
-3 \\ -1 \\ 1 \\ 0 \\ 0
\end{bmatrix}
\quad
\begin{bmatrix}
3 \\ 2 \\ 0 \\ 1 \\ 0
\end{bmatrix}
\quad
\begin{bmatrix}
-1 \\ 0 \\ 0 \\ 0 \\ 1
\end{bmatrix}
\]
C)
\[
\begin{bmatrix}
-5 \\ -1 \\ 1 \\ 0 \\ 0
\end{bmatrix}
\quad
\begin{bmatrix}
7 \\ -2 \\ 0 \\ 1 \\ 0
\end{bmatrix}
\quad
\begin{bmatrix}
2 \\ 1 \\ 0 \\ 0 \\ 1
\end{bmatrix}
\]
D)
\[
\begin{bmatrix}
-5 \\ -1 \\ 1 \\ 0 \\ 0
\end{bmatrix}
\quad
\begin{](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8aa5a8f7-80ac-4340-a2ba-c822c7404ea9%2Fa905881d-53e5-4488-9a64-290a12fa5092%2Fuf0mrp9_processed.png&w=3840&q=75)
Transcribed Image Text:**Topic**: Finding the Null Space of a Matrix
To find an explicit description of the null space of a matrix \( A \), one must identify the vectors that span the null space.
**1) Given Matrix:**
\[
A = \begin{bmatrix}
1 & -2 & 3 & -3 & -1 \\
-2 & 5 & -5 & 4 & 1 \\
-1 & 3 & -2 & 1 & 0
\end{bmatrix}
\]
- **Options for Null Space Vectors:**
A)
\[
\begin{bmatrix}
1 \\ 0 \\ 5 \\ -7 \\ -3
\end{bmatrix}
\quad
\begin{bmatrix}
0 \\ 1 \\ -2 \\ -1 \\ -1
\end{bmatrix}
\]
B)
\[
\begin{bmatrix}
2 \\ 1 \\ 0 \\ 0 \\ 0
\end{bmatrix}
\quad
\begin{bmatrix}
-3 \\ -1 \\ 1 \\ 0 \\ 0
\end{bmatrix}
\quad
\begin{bmatrix}
3 \\ 2 \\ 0 \\ 1 \\ 0
\end{bmatrix}
\quad
\begin{bmatrix}
-1 \\ 0 \\ 0 \\ 0 \\ 1
\end{bmatrix}
\]
C)
\[
\begin{bmatrix}
-5 \\ -1 \\ 1 \\ 0 \\ 0
\end{bmatrix}
\quad
\begin{bmatrix}
7 \\ -2 \\ 0 \\ 1 \\ 0
\end{bmatrix}
\quad
\begin{bmatrix}
2 \\ 1 \\ 0 \\ 0 \\ 1
\end{bmatrix}
\]
D)
\[
\begin{bmatrix}
-5 \\ -1 \\ 1 \\ 0 \\ 0
\end{bmatrix}
\quad
\begin{
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