Give bases for row(A), col(A), and null(A). 1 1 -8 0 2 1 1 -1 -9 row(A) col (A) null(A) A = ↓ 1
Give bases for row(A), col(A), and null(A). 1 1 -8 0 2 1 1 -1 -9 row(A) col (A) null(A) A = ↓ 1
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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![The image provides a matrix \( A \) and instructs on finding bases for the row space, column space, and null space of \( A \).
The matrix \( A \) is given as:
\[
A = \begin{bmatrix} 1 & 1 & -8 \\ 0 & 2 & 1 \\ 1 & -1 & -9 \end{bmatrix}
\]
### Tasks:
1. **row(A):**
- Description: Find a basis for the row space of matrix \( A \).
- Visual: Three blanks or placeholders, indicating room for basis vectors.
- Arrows: Indicate that vectors are derived from the rows of the matrix.
2. **col(A):**
- Description: Find a basis for the column space of matrix \( A \).
- Visual: Four blanks or placeholders, indicating vectors that fill this space.
- Arrows: Indicate that vectors are derived from the columns of the matrix.
3. **null(A):**
- Description: Find a basis for the null space of matrix \( A \).
- Visual: Four blanks or placeholders, indicating vectors that form the null space.
- Arrows: Show the vector directions needed for the null space.
### Explanation of Graphs/Diagrams:
- Each space (row, column, and null) has a diagrammatic representation showing where basis vectors should be placed.
- Green and gray arrows are used to indicate movement or the direction of derivation of these vectors from the matrix.
- The desire is to fill these slots with appropriate vectors derived from computational processes (like row reduction or solving homogeneous equations) for each specific space.
This visualization aids in understanding linear algebra concepts, particularly finding bases for different subspaces associated with a matrix.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1c4c6df5-8b96-455e-b2de-04bdb043521a%2F1259340c-0f1e-4740-9b6f-43ec1722453c%2Fssurd7l_processed.png&w=3840&q=75)
Transcribed Image Text:The image provides a matrix \( A \) and instructs on finding bases for the row space, column space, and null space of \( A \).
The matrix \( A \) is given as:
\[
A = \begin{bmatrix} 1 & 1 & -8 \\ 0 & 2 & 1 \\ 1 & -1 & -9 \end{bmatrix}
\]
### Tasks:
1. **row(A):**
- Description: Find a basis for the row space of matrix \( A \).
- Visual: Three blanks or placeholders, indicating room for basis vectors.
- Arrows: Indicate that vectors are derived from the rows of the matrix.
2. **col(A):**
- Description: Find a basis for the column space of matrix \( A \).
- Visual: Four blanks or placeholders, indicating vectors that fill this space.
- Arrows: Indicate that vectors are derived from the columns of the matrix.
3. **null(A):**
- Description: Find a basis for the null space of matrix \( A \).
- Visual: Four blanks or placeholders, indicating vectors that form the null space.
- Arrows: Show the vector directions needed for the null space.
### Explanation of Graphs/Diagrams:
- Each space (row, column, and null) has a diagrammatic representation showing where basis vectors should be placed.
- Green and gray arrows are used to indicate movement or the direction of derivation of these vectors from the matrix.
- The desire is to fill these slots with appropriate vectors derived from computational processes (like row reduction or solving homogeneous equations) for each specific space.
This visualization aids in understanding linear algebra concepts, particularly finding bases for different subspaces associated with a matrix.
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