3. The matrix A is given below. Find a basis for C(A), R(A), and N(A). Also, find the rank(A) [1 -1 0 -21 2 1 1 3 -1 3 -3 A = 4 4 1 L1 1 1 0
3. The matrix A is given below. Find a basis for C(A), R(A), and N(A). Also, find the rank(A) [1 -1 0 -21 2 1 1 3 -1 3 -3 A = 4 4 1 L1 1 1 0
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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C(A) = column of A
R(A) = row of A
N(A) = null of A
Please help me out. Thank you
![**Problem 3:**
The matrix \( A \) is given below. Find a basis for \( C(A) \), \( R(A) \), and \( N(A) \). Also, find the rank \( \text{rank}(A) \).
\[
A = \begin{bmatrix}
1 & 2 & -1 & 0 & -2 \\
2 & 1 & 1 & 3 & -1 \\
4 & 4 & 1 & 3 & -3 \\
1 & 1 & 1 & 0 & 0
\end{bmatrix}
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Transcribed Image Text:**Problem 3:**
The matrix \( A \) is given below. Find a basis for \( C(A) \), \( R(A) \), and \( N(A) \). Also, find the rank \( \text{rank}(A) \).
\[
A = \begin{bmatrix}
1 & 2 & -1 & 0 & -2 \\
2 & 1 & 1 & 3 & -1 \\
4 & 4 & 1 & 3 & -3 \\
1 & 1 & 1 & 0 & 0
\end{bmatrix}
\]
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