Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Determinants
Section3.CM: Cumulative Review
Problem 17CM: Find the sequence of the elementary matrices whose product is the non singular matrix below. [2410]
Related questions
Question
![**Problem Statement:**
Find a basis for the row space of the matrix
\[
\begin{bmatrix}
8 & 16 & 3 \\
8 & 24 & 8 \\
8 & 8 & -2
\end{bmatrix}
\]
**Answer Choices:**
1. \(\left\{ \begin{pmatrix} 2, 0, -\frac{7}{4} \end{pmatrix}, \begin{pmatrix} 0, 2, \frac{5}{4} \end{pmatrix} \right\}\)
2. \(\left\{ \begin{pmatrix} 2, 0, \frac{7}{4} \end{pmatrix}, \begin{pmatrix} 0, 2, \frac{5}{4} \end{pmatrix}, \begin{pmatrix} 0, 6, \frac{15}{4} \end{pmatrix} \right\}\)
3. \(\left\{ \begin{pmatrix} 0, 2, \frac{5}{4} \end{pmatrix}, \begin{pmatrix} 0, 6, \frac{15}{4} \end{pmatrix} \right\}\)
4. \(\left\{ \begin{pmatrix} 2, 0, \frac{7}{4} \end{pmatrix}, \begin{pmatrix} 6, 0, \frac{21}{4} \end{pmatrix} \right\}\)
5. \(\left\{ \begin{pmatrix} 2, 0, \frac{7}{4} \end{pmatrix}, \begin{pmatrix} 0, 2, \frac{5}{4} \end{pmatrix}, \begin{pmatrix} 6, 0, \frac{21}{4} \end{pmatrix} \right\}\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6dcee43b-a798-4f5f-aaa7-63ced3120c51%2Fe17d9184-4a69-4f2c-b856-e9241ef1e7b9%2Fce6jorj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find a basis for the row space of the matrix
\[
\begin{bmatrix}
8 & 16 & 3 \\
8 & 24 & 8 \\
8 & 8 & -2
\end{bmatrix}
\]
**Answer Choices:**
1. \(\left\{ \begin{pmatrix} 2, 0, -\frac{7}{4} \end{pmatrix}, \begin{pmatrix} 0, 2, \frac{5}{4} \end{pmatrix} \right\}\)
2. \(\left\{ \begin{pmatrix} 2, 0, \frac{7}{4} \end{pmatrix}, \begin{pmatrix} 0, 2, \frac{5}{4} \end{pmatrix}, \begin{pmatrix} 0, 6, \frac{15}{4} \end{pmatrix} \right\}\)
3. \(\left\{ \begin{pmatrix} 0, 2, \frac{5}{4} \end{pmatrix}, \begin{pmatrix} 0, 6, \frac{15}{4} \end{pmatrix} \right\}\)
4. \(\left\{ \begin{pmatrix} 2, 0, \frac{7}{4} \end{pmatrix}, \begin{pmatrix} 6, 0, \frac{21}{4} \end{pmatrix} \right\}\)
5. \(\left\{ \begin{pmatrix} 2, 0, \frac{7}{4} \end{pmatrix}, \begin{pmatrix} 0, 2, \frac{5}{4} \end{pmatrix}, \begin{pmatrix} 6, 0, \frac{21}{4} \end{pmatrix} \right\}\)
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