Find the change of basis matrix [B]&• 2 B = { []}]} <= { [4] []} C 7 8 23 10 71 40 4 10 8 40
Find the change of basis matrix [B]&• 2 B = { []}]} <= { [4] []} C 7 8 23 10 71 40 4 10 8 40
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
![The given task is to find the change of basis matrix \([\mathcal{B}]_{\mathcal{C}}\).
The bases are:
\[
\mathcal{B} = \left\{ \begin{bmatrix} 9 \\ 5 \end{bmatrix}, \begin{bmatrix} 2 \\ 7 \end{bmatrix} \right\}
\]
\[
\mathcal{C} = \left\{ \begin{bmatrix} 7 \\ -4 \end{bmatrix}, \begin{bmatrix} -4 \\ 8 \end{bmatrix} \right\}
\]
The change of basis matrix \([\mathcal{B}]_{\mathcal{C}}\) is specified as:
\[
\begin{bmatrix}
\frac{23}{10} & \frac{4}{10} \\
\frac{71}{40} & \frac{8}{40}
\end{bmatrix}
\]
This matrix is used to transform coordinate vectors from the basis \(\mathcal{C}\) to the basis \(\mathcal{B}\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc5d85aee-a1f7-49d7-bd5c-1a09c98e68fd%2Fda84e9a7-0014-4d99-bf98-e104162f1ab8%2F3f2ubwe_processed.png&w=3840&q=75)
Transcribed Image Text:The given task is to find the change of basis matrix \([\mathcal{B}]_{\mathcal{C}}\).
The bases are:
\[
\mathcal{B} = \left\{ \begin{bmatrix} 9 \\ 5 \end{bmatrix}, \begin{bmatrix} 2 \\ 7 \end{bmatrix} \right\}
\]
\[
\mathcal{C} = \left\{ \begin{bmatrix} 7 \\ -4 \end{bmatrix}, \begin{bmatrix} -4 \\ 8 \end{bmatrix} \right\}
\]
The change of basis matrix \([\mathcal{B}]_{\mathcal{C}}\) is specified as:
\[
\begin{bmatrix}
\frac{23}{10} & \frac{4}{10} \\
\frac{71}{40} & \frac{8}{40}
\end{bmatrix}
\]
This matrix is used to transform coordinate vectors from the basis \(\mathcal{C}\) to the basis \(\mathcal{B}\).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
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,
