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Given the vector functions 6 4t ·[³7] ₁-4 are solutions to a 2 × 2 constant-coefficient differential system, a) compute the Wronkskian of {y₁, y₂}. W(t) = У1 = 2t Y(t) = = and Y2 b) Are {y₁, y2} are linearly independent? O Yes, {yı, y2} are linearly independent. O No, {y1, y2} are linearly dependent. = c) Determine the fundamental matrix of the system.

Given the vector functions 6 4t ·[³7] ₁-4 are solutions to a 2 × 2 constant-coefficient differential system, a) compute the Wronkskian of {y₁, y₂}. W(t) = У1 = 2t Y(t) = = and Y2 b) Are {y₁, y2} are linearly independent? O Yes, {yı, y2} are linearly independent. O No, {y1, y2} are linearly dependent. = c) Determine the fundamental matrix of the system.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...
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Given the vector functions 6 ·[³7]₁-4 are solutions to a 2 x 2 constant-coefficient differential system, a) compute the Wronkskian of {y₁, y2}. W (t) = У1 = [*]e- Y(t) = = 2t and Y2 b) Are {y₁, y2} are linearly independent? O Yes, {y1, y2} are linearly independent. O No, {y1, y2} are linearly dependent. = c) Determine the fundamental matrix of the system. 4t
Transcribed Image Text:Given the vector functions 6 ·[³7]₁-4 are solutions to a 2 x 2 constant-coefficient differential system, a) compute the Wronkskian of {y₁, y2}. W (t) = У1 = [*]e- Y(t) = = 2t and Y2 b) Are {y₁, y2} are linearly independent? O Yes, {y1, y2} are linearly independent. O No, {y1, y2} are linearly dependent. = c) Determine the fundamental matrix of the system. 4t
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