Suppose A has row echelon form - 8 - 36 - 36 0 0 0 - 0 0 6 8 – 40 0 - 9 5 6 - 12 The following row operations transform A into this matrix: First, perform the row operation 5R₁ → R₁, . Second, perform the row operation - 4R4 R4, Third, perform the row operation 4R3 + R₁ → R₁, Finally, perform the row operation 3R3 R4 → R₁,
Suppose A has row echelon form - 8 - 36 - 36 0 0 0 - 0 0 6 8 – 40 0 - 9 5 6 - 12 The following row operations transform A into this matrix: First, perform the row operation 5R₁ → R₁, . Second, perform the row operation - 4R4 R4, Third, perform the row operation 4R3 + R₁ → R₁, Finally, perform the row operation 3R3 R4 → R₁,
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
Find what |A| = of matrix image below
![### Matrix in Row Echelon Form
Consider the matrix \( A \) in row echelon form:
\[
\begin{bmatrix}
-36 & -8 & 6 & 9 \\
0 & -36 & 8 & -5 \\
0 & 0 & -40 & 6 \\
0 & 0 & 0 & -12 \\
\end{bmatrix}
\]
### Row Operations to Transform Matrix \( A \)
The following sequence of row operations transforms matrix \( A \) into a different matrix:
1. **First Operation:** Multiply the first row by 5:
\[
5R_1 \rightarrow R_1
\]
2. **Second Operation:** Multiply the fourth row by \(-4\):
\[
-4R_4 \rightarrow R_4
\]
3. **Third Operation:** Add 4 times the third row to the first row:
\[
4R_3 + R_1 \rightarrow R_1
\]
4. **Fourth Operation:** Add 3 times the third row to the fourth row:
\[
3R_3 + R_4 \rightarrow R_4
\]
These operations are used to simplify the matrix further or achieve a specific form, such as reduced row echelon form.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F181283bb-83dc-4f09-86f1-fac04e6d4723%2Fa036d795-cc19-4a47-977b-f3b682e8669f%2Fii4m9vs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Matrix in Row Echelon Form
Consider the matrix \( A \) in row echelon form:
\[
\begin{bmatrix}
-36 & -8 & 6 & 9 \\
0 & -36 & 8 & -5 \\
0 & 0 & -40 & 6 \\
0 & 0 & 0 & -12 \\
\end{bmatrix}
\]
### Row Operations to Transform Matrix \( A \)
The following sequence of row operations transforms matrix \( A \) into a different matrix:
1. **First Operation:** Multiply the first row by 5:
\[
5R_1 \rightarrow R_1
\]
2. **Second Operation:** Multiply the fourth row by \(-4\):
\[
-4R_4 \rightarrow R_4
\]
3. **Third Operation:** Add 4 times the third row to the first row:
\[
4R_3 + R_1 \rightarrow R_1
\]
4. **Fourth Operation:** Add 3 times the third row to the fourth row:
\[
3R_3 + R_4 \rightarrow R_4
\]
These operations are used to simplify the matrix further or achieve a specific form, such as reduced row echelon form.
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