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24U₂ Use linearization (either with the Jacobian matrix or a change of variables defined by a translation....though you could do both dz=y-x² Yes, you for practice!) to classify the equilibrium point at Y₁ = (x, y) = (1, 1) for the nonlinear system { dy y-x can also determine/check the answer with StreamPlot on Mathematica, but I would encourage you to do it symbolically both ways mentioned above. Select one: O a. Yo = (x, y) = (1, 1) is a real (non-spiral) sink. O b. O c. Yo = (x, y) = (1, 1) is a spiral source. O d. Yo = (x, y) = (1, 1) is a spiral sink. Check Yo = (x, y) = (1, 1) is a saddle point. which theorem justifies the use of linearization (with a Jacobian matrix) to classify a hyperbolic equilibrium point Yg of a nonlinear system = F(Y)? Select one: O a. Existence and Uniqueness Theorem O b. Poincaré-Bendixson Theorem O c. Spectral Theorem O d. Hartman-Grobman Theorem Check CAn orthogonal matrix P has orthonormal columns and orthonormal rows. Select one: O True O False

24U₂ Use linearization (either with the Jacobian matrix or a change of variables defined by a translation....though you could do both dz=y-x² Yes, you for practice!) to classify the equilibrium point at Y₁ = (x, y) = (1, 1) for the nonlinear system { dy y-x can also determine/check the answer with StreamPlot on Mathematica, but I would encourage you to do it symbolically both ways mentioned above. Select one: O a. Yo = (x, y) = (1, 1) is a real (non-spiral) sink. O b. O c. Yo = (x, y) = (1, 1) is a spiral source. O d. Yo = (x, y) = (1, 1) is a spiral sink. Check Yo = (x, y) = (1, 1) is a saddle point. which theorem justifies the use of linearization (with a Jacobian matrix) to classify a hyperbolic equilibrium point Yg of a nonlinear system = F(Y)? Select one: O a. Existence and Uniqueness Theorem O b. Poincaré-Bendixson Theorem O c. Spectral Theorem O d. Hartman-Grobman Theorem Check CAn orthogonal matrix P has orthonormal columns and orthonormal rows. Select one: O True O False

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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24 Use Use linearization (either with the Jacobian matrix or a change of variables defined by a translation....though you could do both =y=x² for practice!) to classify the equilibrium point at Y₁ = (x, y) = (1, 1) for the nonlinear system Yes, you dy =y-x dt can also determine/check the answer with StreamPlot on Mathematica, but I would encourage you to do it symbolically both ways mentioned above. Select one: O a. Yo = (x, y) = (1, 1) is a real (non-spiral) sink. O b. Yo = (x, y) = (1, 1) is a saddle point. O c. Yo = (x, y) = (1, 1) is a spiral source. O d. Yo = (x, y) = (1, 1) is a spiral sink. Check which theorem justifies the use of linearization (with a Jacobian matrix) to classify a hyperbolic equilibrium point Y₁ of a nonlinear system d = F(Y)? Select one: O a. Existence and Uniqueness Theorem O b. Poincaré-Bendixson Theorem O c. Spectral Theorem O d. Hartman-Grobman Theorem Check C An orthogonal matrix P has orthonormal columns and orthonormal rows. Select one: O True O False
Transcribed Image Text:24 Use Use linearization (either with the Jacobian matrix or a change of variables defined by a translation....though you could do both =y=x² for practice!) to classify the equilibrium point at Y₁ = (x, y) = (1, 1) for the nonlinear system Yes, you dy =y-x dt can also determine/check the answer with StreamPlot on Mathematica, but I would encourage you to do it symbolically both ways mentioned above. Select one: O a. Yo = (x, y) = (1, 1) is a real (non-spiral) sink. O b. Yo = (x, y) = (1, 1) is a saddle point. O c. Yo = (x, y) = (1, 1) is a spiral source. O d. Yo = (x, y) = (1, 1) is a spiral sink. Check which theorem justifies the use of linearization (with a Jacobian matrix) to classify a hyperbolic equilibrium point Y₁ of a nonlinear system d = F(Y)? Select one: O a. Existence and Uniqueness Theorem O b. Poincaré-Bendixson Theorem O c. Spectral Theorem O d. Hartman-Grobman Theorem Check C An orthogonal matrix P has orthonormal columns and orthonormal rows. Select one: O True O False
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