Let A be a matrix and v be a vector given as follows: 1 1 1 1 0011 0011 0000 A = -| V = Determine if v is in Col(A), where Col(A) is the column space of A. Determine if v is in Nul(A), where Nul(A) is the null space of A. Find an explicit description of Nul(A) by listing vectors that span the null space.
Let A be a matrix and v be a vector given as follows: 1 1 1 1 0011 0011 0000 A = -| V = Determine if v is in Col(A), where Col(A) is the column space of A. Determine if v is in Nul(A), where Nul(A) is the null space of A. Find an explicit description of Nul(A) by listing vectors that span the null space.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![1. Let \( A \) be a matrix and \( v \) be a vector given as follows:
\[
A = \begin{bmatrix}
1 & 1 & 1 & 1 \\
0 & 0 & 1 & 1 \\
0 & 0 & 1 & 1 \\
0 & 0 & 0 & 0
\end{bmatrix}
\quad
v = \begin{bmatrix}
1 \\
-1 \\
-1 \\
1
\end{bmatrix}
\]
a) Determine if \( v \) is in \( \text{Col}(A) \), where \( \text{Col}(A) \) is the column space of \( A \).
b) Determine if \( v \) is in \( \text{Nul}(A) \), where \( \text{Nul}(A) \) is the null space of \( A \).
c) Find an explicit description of \( \text{Nul}(A) \) by listing vectors that span the null space.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb493ecdd-cbdc-400d-a05a-de2010eb2d52%2F71031ed1-4613-4a0e-87e5-9ef279a7b603%2Fl2iga28_processed.png&w=3840&q=75)
Transcribed Image Text:1. Let \( A \) be a matrix and \( v \) be a vector given as follows:
\[
A = \begin{bmatrix}
1 & 1 & 1 & 1 \\
0 & 0 & 1 & 1 \\
0 & 0 & 1 & 1 \\
0 & 0 & 0 & 0
\end{bmatrix}
\quad
v = \begin{bmatrix}
1 \\
-1 \\
-1 \\
1
\end{bmatrix}
\]
a) Determine if \( v \) is in \( \text{Col}(A) \), where \( \text{Col}(A) \) is the column space of \( A \).
b) Determine if \( v \) is in \( \text{Nul}(A) \), where \( \text{Nul}(A) \) is the null space of \( A \).
c) Find an explicit description of \( \text{Nul}(A) \) by listing vectors that span the null space.
Expert Solution
Ideas
Recall Col(A) is linear combination of column space.
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