0 3 1 000 3 [10 0 0 2 0 6 0 0 1 0 -3 2 0 00 0 0 -3 3 0 0 0 1 -3 0 6 0 000 0 Find a basis for the row space of A, a basis for the column space of A, and the rank of A. The reduced row echelon form of the matrix A = (a) Row space basis: (b) Column space basis: (c) Rank:

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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The reduced row echelon form of the matrix \( A \) is

\[ A = \begin{bmatrix}
1 & 0 & 0 & 0 & 3 \\
2 & 0 & 0 & 0 & 6 \\
0 & 2 & -3 & 3 \\
0 & -2 & 0 & 6 \\
\end{bmatrix} \]

The reduced row echelon form is 

\[ \begin{bmatrix}
1 & 0 & 0 & 0 & 3 \\
0 & 0 & 0 & 0 & 3 \\
0 & 0 & 1 & 0 & -3 \\
0 & 0 & 0 & 0 & 0 \\
\end{bmatrix} \]

Find a basis for the row space of \( A \), a basis for the column space of \( A \), and the rank of \( A \).

(a) Row space basis:  
\(\boxed{\;}

(b) Column space basis:  
\(\boxed{\;}

(c) Rank:  
\(\boxed{\;}
Transcribed Image Text:The reduced row echelon form of the matrix \( A \) is \[ A = \begin{bmatrix} 1 & 0 & 0 & 0 & 3 \\ 2 & 0 & 0 & 0 & 6 \\ 0 & 2 & -3 & 3 \\ 0 & -2 & 0 & 6 \\ \end{bmatrix} \] The reduced row echelon form is \[ \begin{bmatrix} 1 & 0 & 0 & 0 & 3 \\ 0 & 0 & 0 & 0 & 3 \\ 0 & 0 & 1 & 0 & -3 \\ 0 & 0 & 0 & 0 & 0 \\ \end{bmatrix} \] Find a basis for the row space of \( A \), a basis for the column space of \( A \), and the rank of \( A \). (a) Row space basis: \(\boxed{\;} (b) Column space basis: \(\boxed{\;} (c) Rank: \(\boxed{\;}
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