Row reduce the matrices in Exercises 3 and 4 to reduced echelon fom. Circle the pivol posilions in the final matrix and m the original matrix, and list the pivol columns, 4. 4. 8. 3. 2. 9. 8. 12 4. 4. 9. 6.
Row reduce the matrices in Exercises 3 and 4 to reduced echelon fom. Circle the pivol posilions in the final matrix and m the original matrix, and list the pivol columns, 4. 4. 8. 3. 2. 9. 8. 12 4. 4. 9. 6.
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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Number 4
![### CHAPTER 1: Linear Equations in Linear Algebra
**2.**
a.
\[ \begin{bmatrix}
0 & 0 & 1 & 1 \\
0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0
\end{bmatrix} \]
b.
\[ \begin{bmatrix}
1 & 0 & 0 & 0 \\
0 & 2 & 0 & 0 \\
0 & 0 & 1 & 1
\end{bmatrix} \]
c.
\[ \begin{bmatrix}
1 & 0 & 0 \\
0 & 2 & 0 \\
0 & 0 & 0 \\
0 & 0 & 1
\end{bmatrix} \]
d.
\[ \begin{bmatrix}
0 & 1 & 1 \\
0 & 1 & 1 \\
0 & 0 & 0 \\
0 & 0 & 0
\end{bmatrix} \]
**Row reduce the matrices in Exercises 3 and 4 to reduced echelon form. Circle the pivot positions in the final matrix and in the original matrix, and list the pivot columns.**
**3.**
\[ \begin{bmatrix}
1 & 2 & 4 & 8 \\
2 & 4 & 5 & 4 \\
3 & 6 & 9 & 12
\end{bmatrix} \]
**4.**
\[ \begin{bmatrix}
1 & 2 & 4 & 5 \\
2 & 4 & 5 & 4 \\
4 & 2 & 5 & 6
\end{bmatrix} \]
**5. Describe the possible echelon forms of a nonzero 2 x 2 matrix. Use the symbols *, and 0, as in the first part of Example 1.**
**6. Repeat Exercise 5 for a nonzero 3 x 2 matrix.**
**Find the general solutions of the systems whose augmented matrices are given in Exercises 7-14.**
**7.**
\[ \begin{bmatrix}
1 & 3 & 4 \\
3 & 9 & 7](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fee22cf2f-b974-4b00-a3cf-09b388e7d65d%2Ffab69458-32d7-4f72-90f9-31ccfa5cb7b1%2F72rkwyl.jpeg&w=3840&q=75)
Transcribed Image Text:### CHAPTER 1: Linear Equations in Linear Algebra
**2.**
a.
\[ \begin{bmatrix}
0 & 0 & 1 & 1 \\
0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0
\end{bmatrix} \]
b.
\[ \begin{bmatrix}
1 & 0 & 0 & 0 \\
0 & 2 & 0 & 0 \\
0 & 0 & 1 & 1
\end{bmatrix} \]
c.
\[ \begin{bmatrix}
1 & 0 & 0 \\
0 & 2 & 0 \\
0 & 0 & 0 \\
0 & 0 & 1
\end{bmatrix} \]
d.
\[ \begin{bmatrix}
0 & 1 & 1 \\
0 & 1 & 1 \\
0 & 0 & 0 \\
0 & 0 & 0
\end{bmatrix} \]
**Row reduce the matrices in Exercises 3 and 4 to reduced echelon form. Circle the pivot positions in the final matrix and in the original matrix, and list the pivot columns.**
**3.**
\[ \begin{bmatrix}
1 & 2 & 4 & 8 \\
2 & 4 & 5 & 4 \\
3 & 6 & 9 & 12
\end{bmatrix} \]
**4.**
\[ \begin{bmatrix}
1 & 2 & 4 & 5 \\
2 & 4 & 5 & 4 \\
4 & 2 & 5 & 6
\end{bmatrix} \]
**5. Describe the possible echelon forms of a nonzero 2 x 2 matrix. Use the symbols *, and 0, as in the first part of Example 1.**
**6. Repeat Exercise 5 for a nonzero 3 x 2 matrix.**
**Find the general solutions of the systems whose augmented matrices are given in Exercises 7-14.**
**7.**
\[ \begin{bmatrix}
1 & 3 & 4 \\
3 & 9 & 7
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