By calculating the eigenvalues (and if needed the eigenvectors) of the matrix A, determine the nature of the critical point (0,0) of z' = Az for the ollowing six 2 x 2 matrices A. Your choices here are; node (stable or unstable), saddle, spiral point (stable or unstable), center, degenerate node with one eigenvector (stable or unstable), and degenerate node with two eigenvectors (stable or unstable0. Find also the polar equations, and sketch the trajectories including the directions, for each of these systems 0 0 -7 0

By calculating the eigenvalues (and if needed the eigenvectors) of the matrix A, determine the nature of the critical point (0,0) of z' = Az for the ollowing six 2 x 2 matrices A. Your choices here are; node (stable or unstable), saddle, spiral point (stable or unstable), center, degenerate node with one eigenvector (stable or unstable), and degenerate node with two eigenvectors (stable or unstable0. Find also the polar equations, and sketch the trajectories including the directions, for each of these systems 0 0 -7 0

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

pls explain to step by step and dont skip any steps. thanks

By calculating the eigenvalues (and if needed the eigenvectors) of the
matrix A, determine the nature of the critical point (0,0) of z' = Az for the ollowing
six 2 x 2 matrices A. Your choices here are; node (stable or unstable), saddle, spiral
point (stable or unstable), center, degenerate node with one eigenvector (stable or
unstable), and degenerate node with two eigenvectors (stable or unstable0. Find also
the polar equations, and sketch the trajectories including the directions, for each of
these systems
0
0 -7
0

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