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onsider the linear system A₁ = 0 v1 = ÿ₁(t) = a. Find the eigenvalues and eigenvectors for the coefficient matrix. TE 3 = -2t y' -2 3t = -3 6 -21 " ÿ. and X₂ 1 b. For each eigenpair in the previous part, form a solution of y'= Ay. Use t as the independent variable in your answers. and ₂(t): = -1t V2: 2t = -1 2 c. Does the set of solutions you found form a fundamental set (i.e., linearly independent set) of solutions? Yes, it is a fundamental set

onsider the linear system A₁ = 0 v1 = ÿ₁(t) = a. Find the eigenvalues and eigenvectors for the coefficient matrix. TE 3 = -2t y' -2 3t = -3 6 -21 " ÿ. and X₂ 1 b. For each eigenpair in the previous part, form a solution of y'= Ay. Use t as the independent variable in your answers. and ₂(t): = -1t V2: 2t = -1 2 c. Does the set of solutions you found form a fundamental set (i.e., linearly independent set) of solutions? Yes, it is a fundamental set

Advanced Engineering Mathematics
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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Consider the linear system A₁ = a. Find the eigenvalues and eigenvectors for the coefficient matrix. = 0 , V1 = 1(t) = = -2t -2 3t v=13&v 3 y. " and X2 = 1 b. For each eigenpair in the previous part, form a solution of ÿ' = Aÿ. Use t as the independent variable in your answers. and y₂(t) = -1t , V₂ 2t || -1 2 c. Does the set of solutions you found form a fundamental set (i.e., linearly independent set) of solutions? Yes, it is a fundamental set +
Transcribed Image Text:Consider the linear system A₁ = a. Find the eigenvalues and eigenvectors for the coefficient matrix. = 0 , V1 = 1(t) = = -2t -2 3t v=13&v 3 y. " and X2 = 1 b. For each eigenpair in the previous part, form a solution of ÿ' = Aÿ. Use t as the independent variable in your answers. and y₂(t) = -1t , V₂ 2t || -1 2 c. Does the set of solutions you found form a fundamental set (i.e., linearly independent set) of solutions? Yes, it is a fundamental set +
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