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1 R = ($I - A)¹=[] s²+1 S

1 R = ($I - A)¹=[] s²+1 S

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Inverse of the Matrix for Academic Applications --- #### Q1: Resolvent Calculation Find the **resolvent \( R \)** for this system, which involves calculating the **inverse** of the matrix \( (sI - A) \). One of the components has been provided. A common factor is already placed in front of the matrix. --- **Question 1**: \[ R = (sI - A)^{-1} = \frac{1}{s^2 + 1} \cdot \begin{bmatrix} s & ? \\ ? & ? \end{bmatrix} \] --- #### Explanation of Components: - **Resolvent (\( R \))**: The resolvent of the matrix \( A \) is defined as \( R = (sI - A)^{-1} \). - **\( s \)**: A scalar variable. - **Matrix \( (sI - A)^{-1} \)**: The inverse of the matrix formed by subtracting \( A \) from \( s \) times the identity matrix \( I \). - **Common Factor**: \( \frac{1}{s^2 + 1} \) The matrix \( \begin{bmatrix} s & ? \\ ? & ? \end{bmatrix} \) must be completed by calculating each unknown entry.
Transcribed Image Text:### Inverse of the Matrix for Academic Applications --- #### Q1: Resolvent Calculation Find the **resolvent \( R \)** for this system, which involves calculating the **inverse** of the matrix \( (sI - A) \). One of the components has been provided. A common factor is already placed in front of the matrix. --- **Question 1**: \[ R = (sI - A)^{-1} = \frac{1}{s^2 + 1} \cdot \begin{bmatrix} s & ? \\ ? & ? \end{bmatrix} \] --- #### Explanation of Components: - **Resolvent (\( R \))**: The resolvent of the matrix \( A \) is defined as \( R = (sI - A)^{-1} \). - **\( s \)**: A scalar variable. - **Matrix \( (sI - A)^{-1} \)**: The inverse of the matrix formed by subtracting \( A \) from \( s \) times the identity matrix \( I \). - **Common Factor**: \( \frac{1}{s^2 + 1} \) The matrix \( \begin{bmatrix} s & ? \\ ? & ? \end{bmatrix} \) must be completed by calculating each unknown entry.
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