### Problem StatementAssume that matrix \( A \) is row equivalent to matrix \( B \). Find bases for Null space of \( A \) (Nul \( A \)), Column space of \( A \) (Col \( A \)), and Row space of \( A \) (Row \( A \)).### Given Matrices\[ A = \begin{bmatrix} -2 & 8 & -2 & -8 \\ 2 & -12 & -4 & 2 \\ -3 & 16 & 3 & -6 \end{bmatrix}, \quad B = \begin{bmatrix} 1 & 0 & 7 & 10 \\ 0 & 4 & 6 & 6 \\ 0 & 0 & 0 & 0 \end{bmatrix} \]### InstructionsCalculate the following:1. **Basis for Null space of \( A \)** (Nul \( A \))2. **Basis for Column space of \( A \)** (Col \( A \))3. **Basis for Row space of \( A \)** (Row \( A \))### ExplanationInclude detailed steps for calculating each base. ### Placeholder for AnswerA column vector basis for Nul \( A \) is \(\boxed{\hspace{4cm}}\). (Use a comma to separate vectors as needed.)**Note**: Provide solutions step-by-step using row reduction, matrix operations, and concepts of linear algebra as required.

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Assume that A is row equivalent to B. Find bases for Nul A, Col A, and Row A. A= -2 8 2 -8 2-12 - 4 - 3 16 3-6 2, B= 1 0 7 10 046 6 000 0 A column vector basis for Nul A is.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

### Problem Statement

Assume that matrix \( A \) is row equivalent to matrix \( B \). Find bases for Null space of \( A \) (Nul \( A \)), Column space of \( A \) (Col \( A \)), and Row space of \( A \) (Row \( A \)).

### Given Matrices
\[
A = \begin{bmatrix}
-2 & 8 & -2 & -8 \\
2 & -12 & -4 & 2 \\
-3 & 16 & 3 & -6
\end{bmatrix},
\quad
B = \begin{bmatrix}
1 & 0 & 7 & 10 \\
0 & 4 & 6 & 6 \\
0 & 0 & 0 & 0
\end{bmatrix}
\]

### Instructions
Calculate the following:
1. **Basis for Null space of \( A \)** (Nul \( A \))
2. **Basis for Column space of \( A \)** (Col \( A \))
3. **Basis for Row space of \( A \)** (Row \( A \))

### Explanation
Include detailed steps for calculating each base.

### Placeholder for Answer
A column vector basis for Nul \( A \) is \(\boxed{\hspace{4cm}}\).
(Use a comma to separate vectors as needed.)

**Note**: Provide solutions step-by-step using row reduction, matrix operations, and concepts of linear algebra as required.

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