The direction field and a few trajectories for a linear system of the form x' = Ax here A is a 2 × 2 matrix are as follows. If ri and r2 denote the eigenvalues of A, the hat can you conclude about rị and r2? ustify your answer enough to convince me you didn't just guess. A. ri and r2 are distinct and positive B. rị and r2 are distinct and negative C. ri and r2 have opposite signs and r2 are complex and have positive real part D. ri

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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The direction field and a few trajectories for a linear system of the form x' = Ax,
where A is a 2 × 2 matrix are as follows. If rị and r2 denote the eigenvalues of A, then
what can you conclude about rị and r2?
Justify your answer enough to convince me you didn't just guess.
A. ri and r2 are distinct and positive
B. rị and r2 are distinct and negative
C. rị and r2 have opposite signs
3
D. ri and r2 are complex and have
positive real part
E. ri and r2 are complex and have
negative real part
F. rị is complex and r2 is negative
-3
-2
-1
1
2
3
...
..A..7...7......
ビ… ビ
オ。
7: 1 1
7.A..
「 、A.22 た。
1 2 11 1: 1 1 1:1
Transcribed Image Text:The direction field and a few trajectories for a linear system of the form x' = Ax, where A is a 2 × 2 matrix are as follows. If rị and r2 denote the eigenvalues of A, then what can you conclude about rị and r2? Justify your answer enough to convince me you didn't just guess. A. ri and r2 are distinct and positive B. rị and r2 are distinct and negative C. rị and r2 have opposite signs 3 D. ri and r2 are complex and have positive real part E. ri and r2 are complex and have negative real part F. rị is complex and r2 is negative -3 -2 -1 1 2 3 ... ..A..7...7...... ビ… ビ オ。 7: 1 1 7.A.. 「 、A.22 た。 1 2 11 1: 1 1 1:1
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