Discrete Mathematics: Introduction to Mathematical Reasoning
1st Edition
ISBN: 9780495826170
Author: Susanna S. Epp
Publisher: Cengage Learning
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Chapter 3.3, Problem 45ES
To determine
To find: The symbolic form of the statement “
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Q1: (8+17 Marks)
(a) If A-[ a ] is a 3x3 matrix; such that a = i (4-2), find the values of
diagonal elements and the value of 2013+ al
(b)
1
20
If D= 3
-6 1
C: third coulum of D and I: unit matrix
1-2
0
5
Find (i) K if CT D' C = 10K
(ii) a and b if adj (D) = a D² + bl
Refer to page 90 for a problem involving the Laplace Transform of a given piecewise function.
Solve it using properties of Laplace Transforms and inverse transforms. Provide a step-by-step
solution with clear calculations.
Instructions: Do not provide irrelevant content. Focus on solving the problem step-by-step and
showing all calculations explicitly for clarity.
Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440 AZF/view?usp=sharing]
On page 83, a power series is given. Use the ratio test or root test to determine the radius of
convergence. Show each calculation clearly, including intermediate steps and final conclusions.
Instructions: Stick to the question. Provide step-by-step calculations for the radius of
convergence and avoid irrelevant content. Ensure the solution is clear and detailed.
Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440AZF/view?usp=sharing]
Chapter 3 Solutions
Discrete Mathematics: Introduction to Mathematical Reasoning
Ch. 3.1 - Prob. 1ESCh. 3.1 - Prob. 2ESCh. 3.1 - Prob. 3ESCh. 3.1 - Prob. 4ESCh. 3.1 - Prob. 5ESCh. 3.1 - Prob. 6ESCh. 3.1 - Prob. 7ESCh. 3.1 - Prob. 8ESCh. 3.1 - Prob. 9ESCh. 3.1 - Prob. 10ES
Ch. 3.1 - Prob. 11ESCh. 3.1 - Prob. 12ESCh. 3.1 - Prob. 13ESCh. 3.1 - Prob. 14ESCh. 3.1 - Prob. 15ESCh. 3.1 - Prob. 16ESCh. 3.1 - Prob. 17ESCh. 3.1 - Prob. 18ESCh. 3.1 - Prob. 19ESCh. 3.1 - Prob. 20ESCh. 3.1 - Prob. 21ESCh. 3.1 - Prob. 22ESCh. 3.1 - Prob. 23ESCh. 3.1 - Prob. 24ESCh. 3.1 - Prob. 25ESCh. 3.1 - Prob. 26ESCh. 3.1 - Prob. 27ESCh. 3.1 - Prob. 28ESCh. 3.1 - Prob. 29ESCh. 3.1 - Prob. 30ESCh. 3.1 - Prob. 31ESCh. 3.1 - Prob. 32ESCh. 3.1 - Prob. 33ESCh. 3.2 - Prob. 1ESCh. 3.2 - Prob. 2ESCh. 3.2 - Prob. 3ESCh. 3.2 - Prob. 4ESCh. 3.2 - Prob. 5ESCh. 3.2 - Prob. 6ESCh. 3.2 - Prob. 7ESCh. 3.2 - Prob. 8ESCh. 3.2 - Prob. 9ESCh. 3.2 - Prob. 10ESCh. 3.2 - Prob. 11ESCh. 3.2 - Prob. 12ESCh. 3.2 - Prob. 13ESCh. 3.2 - Prob. 14ESCh. 3.2 - Prob. 15ESCh. 3.2 - Prob. 16ESCh. 3.2 - Prob. 17ESCh. 3.2 - Prob. 18ESCh. 3.2 - Prob. 19ESCh. 3.2 - Prob. 20ESCh. 3.2 - Prob. 21ESCh. 3.2 - Prob. 22ESCh. 3.2 - Prob. 23ESCh. 3.2 - Prob. 24ESCh. 3.2 - Prob. 25ESCh. 3.2 - Prob. 26ESCh. 3.2 - Prob. 27ESCh. 3.2 - Prob. 28ESCh. 3.2 - Prob. 29ESCh. 3.2 - Prob. 30ESCh. 3.2 - Prob. 31ESCh. 3.2 - Prob. 32ESCh. 3.2 - Prob. 33ESCh. 3.2 - Prob. 34ESCh. 3.2 - Prob. 35ESCh. 3.2 - Prob. 36ESCh. 3.2 - Prob. 37ESCh. 3.2 - Prob. 38ESCh. 3.2 - Prob. 39ESCh. 3.2 - Prob. 40ESCh. 3.2 - Prob. 41ESCh. 3.2 - Prob. 42ESCh. 3.2 - Prob. 43ESCh. 3.2 - Prob. 44ESCh. 3.2 - Prob. 45ESCh. 3.2 - Prob. 46ESCh. 3.2 - Prob. 47ESCh. 3.2 - Prob. 48ESCh. 3.3 - Prob. 1ESCh. 3.3 - Prob. 2ESCh. 3.3 - Prob. 3ESCh. 3.3 - Prob. 4ESCh. 3.3 - Prob. 5ESCh. 3.3 - Prob. 6ESCh. 3.3 - Prob. 7ESCh. 3.3 - Prob. 8ESCh. 3.3 - Prob. 9ESCh. 3.3 - Prob. 10ESCh. 3.3 - Prob. 11ESCh. 3.3 - Prob. 12ESCh. 3.3 - Prob. 13ESCh. 3.3 - Prob. 14ESCh. 3.3 - Prob. 15ESCh. 3.3 - Prob. 16ESCh. 3.3 - Prob. 17ESCh. 3.3 - Prob. 18ESCh. 3.3 - Prob. 19ESCh. 3.3 - Prob. 20ESCh. 3.3 - Prob. 21ESCh. 3.3 - Prob. 22ESCh. 3.3 - Prob. 23ESCh. 3.3 - Prob. 24ESCh. 3.3 - Prob. 25ESCh. 3.3 - Prob. 26ESCh. 3.3 - Prob. 27ESCh. 3.3 - Prob. 28ESCh. 3.3 - Prob. 29ESCh. 3.3 - Prob. 30ESCh. 3.3 - Prob. 31ESCh. 3.3 - Prob. 32ESCh. 3.3 - Prob. 33ESCh. 3.3 - Prob. 34ESCh. 3.3 - Prob. 35ESCh. 3.3 - Prob. 36ESCh. 3.3 - Prob. 37ESCh. 3.3 - Prob. 38ESCh. 3.3 - Prob. 39ESCh. 3.3 - Prob. 40ESCh. 3.3 - Prob. 41ESCh. 3.3 - Prob. 42ESCh. 3.3 - Prob. 43ESCh. 3.3 - Prob. 44ESCh. 3.3 - Prob. 45ESCh. 3.3 - Prob. 46ESCh. 3.3 - Prob. 47ESCh. 3.3 - Prob. 48ESCh. 3.3 - Prob. 49ESCh. 3.3 - Prob. 50ESCh. 3.3 - Prob. 51ESCh. 3.3 - Prob. 52ESCh. 3.3 - Prob. 53ESCh. 3.3 - Prob. 54ESCh. 3.4 - Prob. 1ESCh. 3.4 - Prob. 2ESCh. 3.4 - Prob. 3ESCh. 3.4 - Prob. 4ESCh. 3.4 - Prob. 5ESCh. 3.4 - Prob. 6ESCh. 3.4 - Prob. 7ESCh. 3.4 - Prob. 8ESCh. 3.4 - Prob. 9ESCh. 3.4 - Prob. 10ESCh. 3.4 - Prob. 11ESCh. 3.4 - Prob. 12ESCh. 3.4 - Prob. 13ESCh. 3.4 - Prob. 14ESCh. 3.4 - Prob. 15ESCh. 3.4 - Prob. 16ESCh. 3.4 - Prob. 17ESCh. 3.4 - Prob. 18ESCh. 3.4 - Prob. 19ESCh. 3.4 - Prob. 20ESCh. 3.4 - Prob. 21ESCh. 3.4 - Prob. 22ESCh. 3.4 - Prob. 23ESCh. 3.4 - Prob. 24ESCh. 3.4 - Prob. 25ESCh. 3.4 - Prob. 26ESCh. 3.4 - Prob. 27ESCh. 3.4 - Prob. 28ESCh. 3.4 - Prob. 29ESCh. 3.4 - Prob. 30ESCh. 3.4 - Prob. 31ESCh. 3.4 - Prob. 32ESCh. 3.4 - Prob. 33ESCh. 3.4 - Prob. 34ESCh. 3.4 - Prob. 35ESCh. 3.4 - Prob. 36ES
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- On page 95, a proof of the orthogonality of Legendre polynomials is discussed. Reconstruct the proof with detailed steps, using the weighted integral formulation for Legendre polynomials. Instructions: Stick to solving the problem only. Provide a clear outline, detailed steps, and all necessary calculations. Do not add irrelevant content. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440 AZF/view?usp=sharing]arrow_forwardRefer to page 65 for a proof of the Pythagorean trigonometric identity involving squares of sine and cosine. Provide a detailed step-by-step proof with all intermediate calculations. Instructions: Provide only relevant content Outline the proof clearly, demonstrate all steps, and show calculations in detail. Avoid unnecessary explanations. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440AZF/view?usp=sharing]arrow_forwardOn page 93, there is a problem involving a partial differential equation (PDE). Solve it using the method of separation of variables. Provide a detailed explanation of each step, including separation, solving for eigenvalues, and constructing the general solution. Instructions: Focus on the question. Provide clear steps, detailed calculations, and ensure every intermediate result is shown. Irrelevant details are not needed. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440 AZF/view?usp=sharing]arrow_forward
- On page 97, a contour integral problem involving a complex function is provided. Solve it using Cauchy's Integral Formula. Clearly outline the contour, identify singularities, and evaluate the integral step-by-step. Instructions: Stick strictly to the problem. Provide detailed steps for applying Cauchy's formula and show all calculations clearly. Avoid unnecessary explanations. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9q0Hazb9tC440AZF/view?usp=sharing]arrow_forwardRefer to page 55 for a system of linear equations. Solve the system using matrix methods, including Gaussian elimination or inverse matrix methods. Clearly outline each step and show all intermediate calculations. Instructions: Stick strictly to the problem. Provide a clear outline, solve step-by-step, and show all matrix calculations in detail. Avoid irrelevant explanations. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440AZF/view?usp=sharing]arrow_forwardThe exact differential equation problem is discussed on page 62. Verify the exactness of the given equation and solve it step-by-step. Clearly show all calculations, including how exactness is determined. Instructions: Focus strictly on the problem. Provide a detailed step-by-step solution and show all calculations clearly. Irrelevant answers will not be accepted. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharing]arrow_forward
- The second-order linear differential equation problem can be found on page 72 of the file. Solve it using the characteristic equation method and provide a detailed step-by-step solution. Ensure all calculations are shown clearly and concisely. Instructions: Do not provide irrelevant answers. Outline the problem clearly, solve step-by-step, and show all necessary calculations to ensure clarity. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440 AZF/view?usp=sharing]arrow_forwardRefer to page 80 for a problem involving a double integral that requires conversion to polar coordinates. Solve the integral carefully, showing each step of the transformation and calculations. Instructions: Stick to the question. Provide a clear outline, detailed steps for converting to polar coordinates, and show all calculations. Irrelevant answers are not accepted. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharing]arrow_forwardA non-linear differential equation problem is on page 42 of the linked file. Solve the equation clearly, using an appropriate method such as substitution or exact equations. Link: [https://drive.google.com/file/d/1RQ2OZK-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing]arrow_forward
- Check page 48 of the file for a first-order linear differential equation problem. Solve it using integrating factors and provide all steps. Link: [https://drive.google.com/file/d/1RQ 20 ZK-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing]arrow_forwardRefer to page 45 of the following file for a trigonometric proof question involving sum-to- product formulas. Provide a clear step-by-step solution. Link: [https://drive.google.com/file/d/1RQ 20 ZK-LSxp RyejKEMg 1t2q15dbpVLCS/view? usp=sharing]arrow_forwardRefer to page 52 of the linked file for a second-order homogeneous differential equation. Solve it using the characteristic equation method. Link: [https://drive.google.com/file/d/1RQ 20 ZK-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing]arrow_forward
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