Do the columns of the matrix span IR? Select an Answer v 1. 3 3 -3 3 A = -5 -4 3 -1 -4 -4 4 -4 Select an Answer v 2. -4 -7 A = -3 2 6 6 Select an Answer v 3. 5 25 100
Do the columns of the matrix span IR? Select an Answer v 1. 3 3 -3 3 A = -5 -4 3 -1 -4 -4 4 -4 Select an Answer v 2. -4 -7 A = -3 2 6 6 Select an Answer v 3. 5 25 100
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:**
Do the columns of the matrix span \( \mathbb{R}^3 \)?
**Options for Matrix 1:**
\[
A =
\begin{bmatrix}
3 & 3 & 3 \\
-5 & -4 & 3 \\
4 & 4 & -4 \\
\end{bmatrix}
\]
- Select an Answer
**Options for Matrix 2:**
\[
A =
\begin{bmatrix}
-4 & -7 \\
3 & 2 \\
-6 & 6 \\
\end{bmatrix}
\]
- Select an Answer
**Options for Matrix 3:**
\[
A =
\begin{bmatrix}
5 & 25 & 100 \\
5 & 20 & 100 \\
5 & 15 & 60 \\
\end{bmatrix}
\]
- Select an Answer
**Options for Matrix 4:**
\[
A =
\begin{bmatrix}
1 & -2 & -1 \\
4 & 9 & 2 \\
-1 & 0 & 0 \\
\end{bmatrix}
\]
- Select an Answer
**Explanation of the Task:**
You are to determine whether the columns of each given matrix span the vector space \( \mathbb{R}^3 \). This involves checking if the columns of each matrix can generate the entire three-dimensional space through linear combinations. The matrices provided are of different sizes and configurations, and you need to analyze their properties, such as rank or linear independence, to arrive at the answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2192a9f0-1ae9-4ed3-a35b-fc11f1172fc0%2F45b45753-7219-4d13-8dbb-c92533b9872d%2Fekqq0j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
Do the columns of the matrix span \( \mathbb{R}^3 \)?
**Options for Matrix 1:**
\[
A =
\begin{bmatrix}
3 & 3 & 3 \\
-5 & -4 & 3 \\
4 & 4 & -4 \\
\end{bmatrix}
\]
- Select an Answer
**Options for Matrix 2:**
\[
A =
\begin{bmatrix}
-4 & -7 \\
3 & 2 \\
-6 & 6 \\
\end{bmatrix}
\]
- Select an Answer
**Options for Matrix 3:**
\[
A =
\begin{bmatrix}
5 & 25 & 100 \\
5 & 20 & 100 \\
5 & 15 & 60 \\
\end{bmatrix}
\]
- Select an Answer
**Options for Matrix 4:**
\[
A =
\begin{bmatrix}
1 & -2 & -1 \\
4 & 9 & 2 \\
-1 & 0 & 0 \\
\end{bmatrix}
\]
- Select an Answer
**Explanation of the Task:**
You are to determine whether the columns of each given matrix span the vector space \( \mathbb{R}^3 \). This involves checking if the columns of each matrix can generate the entire three-dimensional space through linear combinations. The matrices provided are of different sizes and configurations, and you need to analyze their properties, such as rank or linear independence, to arrive at the answer.
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