The following 2 matrices are row equivalent find a basis for the column space of A find a basis for the null space of A Is the column space B the same as the column space of A? Why?
The following 2 matrices are row equivalent find a basis for the column space of A find a basis for the null space of A Is the column space B the same as the column space of A? Why?
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 following 2 matrices are row equivalent
find a basis for the column space of A
find a basis for the null space of A
Is the column space B the same as the column space of A? Why?
![The image presents two matrices, labeled \( A \) and \( B \).
Matrix \( A \) is a 3x4 matrix, defined as:
\[
A = \begin{pmatrix}
1 & 3 & 4 & 9 \\
2 & 9 & 5 & 3 \\
1 & 6 & 1 & -6
\end{pmatrix}
\]
Matrix \( B \) is a 3x4 matrix, defined as:
\[
B = \begin{pmatrix}
1 & 0 & 7 & 24 \\
0 & 1 & -1 & -5 \\
0 & 0 & 0 & 0
\end{pmatrix}
\]
These matrices are essential components in linear algebra, often used for solving systems of linear equations, transformations, and various applications in mathematics and engineering. The zero row in matrix \( B \) indicates a potential rank deficiency, which can affect solutions in certain contexts.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffbc65777-4b8c-4cea-bc75-b2bca4e42466%2Ffa3f7ce6-8437-49dc-bc03-6bdae50c1628%2F8i3tkil_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image presents two matrices, labeled \( A \) and \( B \).
Matrix \( A \) is a 3x4 matrix, defined as:
\[
A = \begin{pmatrix}
1 & 3 & 4 & 9 \\
2 & 9 & 5 & 3 \\
1 & 6 & 1 & -6
\end{pmatrix}
\]
Matrix \( B \) is a 3x4 matrix, defined as:
\[
B = \begin{pmatrix}
1 & 0 & 7 & 24 \\
0 & 1 & -1 & -5 \\
0 & 0 & 0 & 0
\end{pmatrix}
\]
These matrices are essential components in linear algebra, often used for solving systems of linear equations, transformations, and various applications in mathematics and engineering. The zero row in matrix \( B \) indicates a potential rank deficiency, which can affect solutions in certain contexts.
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