-4- 2i 4+2i RR,+9R, -6– 3i -9+18i 5 5 -1 3i -4- 2i 4+2i| 5 0 -3i 0 3i 0 5 R-→SR;/(-6-31) 1 -1
-4- 2i 4+2i RR,+9R, -6– 3i -9+18i 5 5 -1 3i -4- 2i 4+2i| 5 0 -3i 0 3i 0 5 R-→SR;/(-6-31) 1 -1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
please explain this step for me, I cannot figure out how to get this step
![The image contains a series of matrix operations, specifically elementary row operations on a given matrix. The process is intended to transform the matrix into a different form, likely for solving a system of equations or finding the matrix's reduced row echelon form. Here's a detailed transcription of the matrices and the operations performed:
1. **First Matrix and Operation:**
\[
\begin{bmatrix}
\frac{-4 - 2i}{5} & \frac{4 + 2i}{5} & 0 \\
\frac{-6 - 3i}{5} & \frac{-9 + 18i}{5} & 0 \\
0 & -1 & 3i
\end{bmatrix}
\]
**Row Operation:**
\[
R_2 \rightarrow R_2 + 9R_1
\]
**Transformed Matrix:**
\[
\begin{bmatrix}
\frac{-4 - 2i}{5} & \frac{4 + 2i}{5} & 0 \\
0 & 1 & -3i \\
0 & -1 & 3i
\end{bmatrix}
\]
2. **Second Matrix and Operation:**
**Row Operation:**
\[
R_2 \rightarrow 5R_2(1 - 6 - 3i)
\]
**Final Transformed Matrix:**
\[
\begin{bmatrix}
\frac{-4 - 2i}{5} & \frac{4 + 2i}{5} & 0 \\
0 & 1 & -3i \\
0 & -1 & 3i
\end{bmatrix}
\]
These steps demonstrate how specific row operations, such as replacing a row with a linear combination of itself and another row, adjust the elements to achieve a desired matrix form. The operations involve addition and scalar multiplication of complex numbers.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf7ac4f3-c9e5-426e-a855-51d402583d0c%2Fadfa35fe-fbb4-4cfa-b79e-67e3afa4099c%2Fgvs2rur_processed.png&w=3840&q=75)
Transcribed Image Text:The image contains a series of matrix operations, specifically elementary row operations on a given matrix. The process is intended to transform the matrix into a different form, likely for solving a system of equations or finding the matrix's reduced row echelon form. Here's a detailed transcription of the matrices and the operations performed:
1. **First Matrix and Operation:**
\[
\begin{bmatrix}
\frac{-4 - 2i}{5} & \frac{4 + 2i}{5} & 0 \\
\frac{-6 - 3i}{5} & \frac{-9 + 18i}{5} & 0 \\
0 & -1 & 3i
\end{bmatrix}
\]
**Row Operation:**
\[
R_2 \rightarrow R_2 + 9R_1
\]
**Transformed Matrix:**
\[
\begin{bmatrix}
\frac{-4 - 2i}{5} & \frac{4 + 2i}{5} & 0 \\
0 & 1 & -3i \\
0 & -1 & 3i
\end{bmatrix}
\]
2. **Second Matrix and Operation:**
**Row Operation:**
\[
R_2 \rightarrow 5R_2(1 - 6 - 3i)
\]
**Final Transformed Matrix:**
\[
\begin{bmatrix}
\frac{-4 - 2i}{5} & \frac{4 + 2i}{5} & 0 \\
0 & 1 & -3i \\
0 & -1 & 3i
\end{bmatrix}
\]
These steps demonstrate how specific row operations, such as replacing a row with a linear combination of itself and another row, adjust the elements to achieve a desired matrix form. The operations involve addition and scalar multiplication of complex numbers.
Expert Solution
Step 1
We have the matrix
Now, we need to apply the operation
This means we need to multiply row 2 by
The first element in row 2 is 0. Therefore, multiplying 0 by will result in 0 only.
Step by step
Solved in 2 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
