3 2 Suppose the matrix, A, has eigenvectors and whose eigenvalues are 8, – 2 and 4 respectively. Then, using the same order, A can be written in the form A = PAP-1 where P = and A =
3 2 Suppose the matrix, A, has eigenvectors and whose eigenvalues are 8, – 2 and 4 respectively. Then, using the same order, A can be written in the form A = PAP-1 where P = and A =
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
100%
![Suppose the matrix, \( A \), has eigenvectors
\[
\begin{bmatrix}
3 \\
0 \\
-2
\end{bmatrix},
\begin{bmatrix}
2 \\
1 \\
-2
\end{bmatrix},
\begin{bmatrix}
5 \\
0 \\
-3
\end{bmatrix}
\]
whose eigenvalues are 8, \(-2\) and 4 respectively. Then, using the same order, \( A \) can be written in the form
\[
A = P \Lambda P^{-1}
\]
where
\[
P =
\begin{bmatrix}
\boxed{} & \boxed{} & \boxed{} \\
\boxed{} & \boxed{} & \boxed{} \\
\boxed{} & \boxed{} & \boxed{}
\end{bmatrix}
\]
and
\[
\Lambda =
\begin{bmatrix}
\boxed{} & \boxed{} & \boxed{} \\
\boxed{} & \boxed{} & \boxed{} \\
\boxed{} & \boxed{} & \boxed{}
\end{bmatrix}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F200b2eb6-b630-49f4-95ef-5591909fdfea%2Fd5419d6c-0c6a-4f47-8a2f-fd272aedf3c5%2F8p2da9n_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose the matrix, \( A \), has eigenvectors
\[
\begin{bmatrix}
3 \\
0 \\
-2
\end{bmatrix},
\begin{bmatrix}
2 \\
1 \\
-2
\end{bmatrix},
\begin{bmatrix}
5 \\
0 \\
-3
\end{bmatrix}
\]
whose eigenvalues are 8, \(-2\) and 4 respectively. Then, using the same order, \( A \) can be written in the form
\[
A = P \Lambda P^{-1}
\]
where
\[
P =
\begin{bmatrix}
\boxed{} & \boxed{} & \boxed{} \\
\boxed{} & \boxed{} & \boxed{} \\
\boxed{} & \boxed{} & \boxed{}
\end{bmatrix}
\]
and
\[
\Lambda =
\begin{bmatrix}
\boxed{} & \boxed{} & \boxed{} \\
\boxed{} & \boxed{} & \boxed{} \\
\boxed{} & \boxed{} & \boxed{}
\end{bmatrix}
\]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.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,
