The following 2 matrices are row equivalent find a basis for the column space of Afind a basis for the null space of AIs 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.

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Answered: The following 2 matrices are row…

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.

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