7. find the determinant of the following matriz : 15 -2 4 -5 -3 6 6 -7]
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
These are practice problems for understanding, not a graded assignment.
![### Algebraic Operations with Matrices
**Exercises:**
(ii) Find \(2A + C\). [L1]
(iii) Find \(BC\). [L1]
(iv) Find \(C^T\). [L1]
(v) Find \(5A + 2B\). [L3]
---
### Leslie Matrix Analysis
5. Consider the 2x2 Leslie matrix.
\[
A = \begin{bmatrix}
1 & 4 \\
0.5 & 0
\end{bmatrix}
\]
(i) Find the long-term growth rate of the population.
(ii) Find the long-term population structure for this population.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd6220f22-ea21-4157-ab75-438ca7812702%2F63ee1f29-6e21-4cf4-a539-cee3023d569d%2Fw2vbu8c_processed.png&w=3840&q=75)
Transcribed Image Text:### Algebraic Operations with Matrices
**Exercises:**
(ii) Find \(2A + C\). [L1]
(iii) Find \(BC\). [L1]
(iv) Find \(C^T\). [L1]
(v) Find \(5A + 2B\). [L3]
---
### Leslie Matrix Analysis
5. Consider the 2x2 Leslie matrix.
\[
A = \begin{bmatrix}
1 & 4 \\
0.5 & 0
\end{bmatrix}
\]
(i) Find the long-term growth rate of the population.
(ii) Find the long-term population structure for this population.
![**Question 6: Fixed Point of a Function**
Find the fixed point of \( f(x) \) on the interval \([-1,1]\), where:
\[ f(x) = \left(\frac{5}{3}\right)x - \left(\frac{8}{3}\right)x^3 \]
**Question 7: Determinant of a Matrix**
Find the determinant of the following matrix:
\[
\begin{bmatrix}
-2 & 1 & 4 \\
2 & -5 & 9 \\
-3 & 6 & -7
\end{bmatrix}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd6220f22-ea21-4157-ab75-438ca7812702%2F63ee1f29-6e21-4cf4-a539-cee3023d569d%2Fq9aegi_processed.png&w=3840&q=75)
Transcribed Image Text:**Question 6: Fixed Point of a Function**
Find the fixed point of \( f(x) \) on the interval \([-1,1]\), where:
\[ f(x) = \left(\frac{5}{3}\right)x - \left(\frac{8}{3}\right)x^3 \]
**Question 7: Determinant of a Matrix**
Find the determinant of the following matrix:
\[
\begin{bmatrix}
-2 & 1 & 4 \\
2 & -5 & 9 \\
-3 & 6 & -7
\end{bmatrix}
\]
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