1 9 6 7 6 -6 -9 0 A = 4 -9 6 2 7 2 -9 8 - 2 - 5 2 9 (a) Find k such that Nul(A) is a subspace of R" (b) Find k such that Col(A) is a subspace of R".
1 9 6 7 6 -6 -9 0 A = 4 -9 6 2 7 2 -9 8 - 2 - 5 2 9 (a) Find k such that Nul(A) is a subspace of R" (b) Find k such that Col(A) is a subspace of R".
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
![The image presents a matrix \( A \) along with two questions related to finding the subspace dimensions of the null space and column space of the matrix.
Matrix \( A \):
\[
A = \begin{bmatrix}
1 & 9 & 6 & 7 \\
6 & -6 & -9 & 0 \\
4 & -9 & 6 & 2 \\
7 & 2 & -9 & 8 \\
-2 & -5 & 2 & 9 \\
\end{bmatrix}
\]
Questions:
(a) Find \( k \) such that \(\text{Nul}(A)\) is a subspace of \(\mathbb{R}^k\).
(b) Find \( k \) such that \(\text{Col}(A)\) is a subspace of \(\mathbb{R}^k\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F84cf688c-5562-46a2-a404-4071be093541%2F16fcc14f-9cb3-4d52-8b7b-7cea6d99daa5%2Frgfuau_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image presents a matrix \( A \) along with two questions related to finding the subspace dimensions of the null space and column space of the matrix.
Matrix \( A \):
\[
A = \begin{bmatrix}
1 & 9 & 6 & 7 \\
6 & -6 & -9 & 0 \\
4 & -9 & 6 & 2 \\
7 & 2 & -9 & 8 \\
-2 & -5 & 2 & 9 \\
\end{bmatrix}
\]
Questions:
(a) Find \( k \) such that \(\text{Nul}(A)\) is a subspace of \(\mathbb{R}^k\).
(b) Find \( k \) such that \(\text{Col}(A)\) is a subspace of \(\mathbb{R}^k\).
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