Find an explicit description of Nul A by listing vectors that span the null space. 1 3 -2 -8 1 A= 0 1 - 5 10 000 00 A spanning set for Nul A is . (Use a comma to separate vectors as needed.) 4
Find an explicit description of Nul A by listing vectors that span the null space. 1 3 -2 -8 1 A= 0 1 - 5 10 000 00 A spanning set for Nul A is . (Use a comma to separate vectors as needed.) 4
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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![**Title: Describing the Null Space of Matrix A**
**Problem Statement:**
Find an explicit description of \( \text{Nul } A \) by listing vectors that span the null space.
**Matrix:**
\[ A = \begin{bmatrix} 1 & 3 & -2 & -8 & 1 \\ 0 & 1 & -5 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 \end{bmatrix} \]
**Instruction:**
A spanning set for \( \text{Nul } A \) is \(\boxed{\phantom{write\ vectors\ here}}\).
(Use a comma to separate vectors as needed.)
**Explanation:**
The matrix \( A \) is a \( 3 \times 5 \) matrix. To find the null space, we need to solve the homogeneous system of equations \( A \mathbf{x} = \mathbf{0} \). This involves finding the solutions that make all rows equal to zero.
The presence of the third row, consisting entirely of zeros, indicates that there are free variables, which will lead to non-trivial solutions forming the basis vectors that span \( \text{Nul } A \). Once solved, the vectors will be listed in the specified format.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F08f6f3ae-62d0-4ecf-a7d1-a70a7054db3c%2F876ea71a-5fb6-4f57-86ad-c231525336bf%2Fs6e6is_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Describing the Null Space of Matrix A**
**Problem Statement:**
Find an explicit description of \( \text{Nul } A \) by listing vectors that span the null space.
**Matrix:**
\[ A = \begin{bmatrix} 1 & 3 & -2 & -8 & 1 \\ 0 & 1 & -5 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 \end{bmatrix} \]
**Instruction:**
A spanning set for \( \text{Nul } A \) is \(\boxed{\phantom{write\ vectors\ here}}\).
(Use a comma to separate vectors as needed.)
**Explanation:**
The matrix \( A \) is a \( 3 \times 5 \) matrix. To find the null space, we need to solve the homogeneous system of equations \( A \mathbf{x} = \mathbf{0} \). This involves finding the solutions that make all rows equal to zero.
The presence of the third row, consisting entirely of zeros, indicates that there are free variables, which will lead to non-trivial solutions forming the basis vectors that span \( \text{Nul } A \). Once solved, the vectors will be listed in the specified format.
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