Find bases for the row space, column space and null space of 2 1 3 4 A: = 1 1 2 4 2 4 2 37 68
Find bases for the row space, column space and null space of 2 1 3 4 A: = 1 1 2 4 2 4 2 37 68
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
Find bases for the row space, column space and null space of
![**Objective**: Find bases for the row space, column space, and null space of the matrix \( A \).
**Matrix**:
\[
A = \begin{pmatrix}
1 & 2 & 1 & 3 & 4 \\
1 & 2 & 4 & 3 & 7 \\
2 & 4 & 2 & 6 & 8
\end{pmatrix}
\]
**Approach**:
1. **Row Space**: Use row reduction to find the row echelon form (REF) or reduced row echelon form (RREF) and identify the non-zero rows as a basis for the row space.
2. **Column Space**: Use the original or reduced matrix to identify a basis from the pivot columns.
3. **Null Space**: Solve the homogeneous equation \( Ax = 0 \) to find the set of vectors that form a basis for the null space.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9e43c9db-5d41-4468-b810-f43391b4cd54%2F9e834562-0f14-4a7f-bf08-3004fc72a5df%2F9lj657s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Objective**: Find bases for the row space, column space, and null space of the matrix \( A \).
**Matrix**:
\[
A = \begin{pmatrix}
1 & 2 & 1 & 3 & 4 \\
1 & 2 & 4 & 3 & 7 \\
2 & 4 & 2 & 6 & 8
\end{pmatrix}
\]
**Approach**:
1. **Row Space**: Use row reduction to find the row echelon form (REF) or reduced row echelon form (RREF) and identify the non-zero rows as a basis for the row space.
2. **Column Space**: Use the original or reduced matrix to identify a basis from the pivot columns.
3. **Null Space**: Solve the homogeneous equation \( Ax = 0 \) to find the set of vectors that form a basis for the null space.
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