E&P3 6.2: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The 2x2 matrix of coefficients A of the rhs of the vector differential equation 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 ' = A 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 is:
[right click on a matrix to get Eigenvectors, with the eigenvalues]
[execute the matrix assignment, then go to see its directionfield; repeat for each matrix]
6.1.27: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.2.1: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.2.9: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 that the zero column here is NOT an eigenvector but just a placeholder to fill out the square matrix. This is a defective matrix with only 1 independent real eigenvector.
phaseplots are revealing6.2.9:
The phaseplot showing real eigenvector directions if any: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Here is the final plot together with the single eigenspace line for the matrix of 6.2.9, an example of a defective matrix: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 pattern of solution curves is interesting: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.2.1:
Here is the plot for 6.2.1 with the 2 eigenspaces drawn in, since the second line with slope 1/2 is not so obvious.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Again the solution curves are interesting, the eigenlines divide the plane of initial data up into 4 sectors, in each of which distinct behavior takes place. For example in the narrow sectors both variables have monotonic behavior, and in the wider sectors, both individual variables experience a turnaround, rising and then falling or falling and then rising.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6.1.27: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,216.2.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6.2.21 defective, zero column to fill out the square 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=34LUkncnRhYmxlRyUqcHJvdGVjdGVkRzYmOyIiIiIiI0YmNyQ3JEkiYUc2IkkiYkdGLDckSSJjR0YsSSJkR0YsL0koc3VidHlwZUc2JEYkSShfc3lzbGliR0YsSSdNYXRyaXhHRjM=LV9JLkxpbmVhckFsZ2VicmFHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiJJLUVpZ2VudmVjdG9yc0dGKDYjLUknTWF0cml4R0YlNiMvSSQlaWRHRigiNUEtL3dUMlduVz0=LV9JLkxpbmVhckFsZ2VicmFHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiJJLEVpZ2VudmFsdWVzR0YoNiMtSSdNYXRyaXhHRiU2Iy9JJCVpZEdGKCI1QS0vd1QyV25XPQ==PkklRGlzY0c2IiwmLUknZmFjdG9yRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsKCokSSJhR0YkIiIjIiIiKiZGLkYwSSJkR0YkRjAhIiMqJEYyRi9GMEYwSSNiY0dGJCIiJQ==as long as LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEiY0YnRi9GMi8lK2V4ZWN1dGFibGVHRj1GOQ== are of the same sign (hence nonzero), the discriminant is nonzero and there are two distinct roots. if they are of the opposite signs and large enough in absolute value to make the discriminant negative, we get complex eigenvalues.TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MTc2MDUzNTUwWCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjJSIjIiMiIiEiIiIhIiJGJ0YlTTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MTc5NjIyMjIyWColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiIyIjXiMiIiJeIyEiIkYlTTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MTc2MDU0MDA2WCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjJSIjIiNeIyIiIkYoXiMhIiJGKEYlTTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MTc2MDU0MTU4WCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjJSIjIiMiIiYiIiMhIiUhIiJGJQ==TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MTc5NjQ2MTE4WColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiIyIjIiIiIiIkRiU=TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MTc2MDU0MzEwWCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjJSIjIiMiIiJGJyIiI0YnRiU=TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MTc2MDU0NDYyWCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjJSIjIiMhIiJGJyIiJSIiJEYlTTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MTc5NjQ2MjU0WColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiIyIjIiIiRidGJQ==TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MTc2MDU0NjE0WCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjJSIjIiMiIiMiIiIiIiFGKUYlTTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MTc2MDU0NzY2WCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjJSIjIiMhIiJGJyIiJSIiJEYlTTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MTc5NjQ2MzkwWColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiIyIjLS1JIkRHNiQlKnByb3RlY3RlZEclKF9zeXNsaWJHNiMlI3gxRzYjJSJ0Ry0tRik2IyUjeDJHRi9GJQ==TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MTc5NjUxMzAyWColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiIyIjLCYtJSN4MUc2IyUidEchIiItJSN4MkdGKiIiJSwmRihGLEYtIiIkRiU=TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MTc5NjUxNDM4WColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiIyIjLS1JIkRHNiQlKnByb3RlY3RlZEclKF9zeXNsaWJHNiMlI3gxRzYjJSJ0Ry0tRik2IyUjeDJHRi9GJQ==TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MTc5NjUxNTc0WColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiIyIjLCYtJSN4MUc2IyUidEciIiYtJSN4MkdGKiEiJSwmRigiIiNGLSEiIkYlTTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MTc2MDU1MDcwWCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjJSIjIiMiIiEiIiIhIiJGJ0YlTTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MTc5NjUxNzEwWColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiIyIjLS1JIkRHNiQlKnByb3RlY3RlZEclKF9zeXNsaWJHNiMlI3gxRzYjJSJ0Ry0tRik2IyUjeDJHRi9GJQ==TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MTc5NjUxODQ2WColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiIyIjLCQtJSN4Mkc2IyUidEchIiItJSN4MUdGKkYlTTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MTc2MDU1Mzc0WCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjKiIkIiQiIiIiIiFGKCIiJCIiI0YoRihGKEYqRiU=TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MTc5NjUxOTgyWColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiJCIkIiIjRiciIiJGJQ==TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MTc2MDU1NTI2WCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjKiIkIiQiIiFGJyIiIiIiJEYoRidGKEYnRidGJQ==TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MTc2MDU1ODMwWCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjKiIkIiQiIiEhIiJGKCIiIiIiI0YpRidGJ0YpRiU=TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MTc5NjUyNjYyWColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiJCIkIiIiRidGJ0YlTTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MTc2MDU1OTgyWCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjKiIkIiQiIiFGJyIiIkYoRihGJ0YnRidGJ0YlTTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MTc2MDM5NzQyWCwlKWFueXRoaW5nRzYiRiVbZ2whIiUhISEjJSIjIiMmJSJtRzYkIiIiRikmRic2JCIiI0YpJkYnNiRGKUYsJkYnNiRGLEYsRiU=TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MTc2MDQwMjIyWCwlKWFueXRoaW5nRzYiRiVbZ2whIiUhISEjJSIjIiMlImFHJSJjRyUiYkclImRHRiU=TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MjEwMTE1NTgyWColKmFsZ2VicmFpY0c2IkYlW2dsISMlISEhIiMiIywoJSJkRyMiIiIiIiMlImFHRigqJHorNiZGKyUiYkclImNHRidbW1tbW1tbW1tdW1ttRilcW1tbW1tbW1tcW1ttISIjW1tbXFtbXFtbW1tbbSIiJV1bW1tbW1tbW1tbW21GKUYoRigsKEYnRihGK0YoRiwjISIiRipGJQ==TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MjEwMTE1NzAyWCwlKmFsZ2VicmFpY0c2IkYlW2dsISIlISEhIyUiIyIjKiYlImJHIiIiLCglImRHI0YoIiIjJSJhRyMhIiJGLCokeis2JkYtRiclImNHRipbW1tbW1tbW1tdW1ttRihcW1tbW1tbW1tcW1ttISIjW1tbXFtbXFtbW1tbbSIiJV1bW1tbW1tbW1tbW21GKEYrRitGL0YoKiZGJ0YoLChGKkYrRi1GLkYwRi5GL0YoRiU=TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ0MDc0MjEwMTM2NTQyWColKWFueXRoaW5nRzYiRiVbZ2whIyUhISEiIyIjLCglImRHIyIiIiIiIyUiYUdGKCokeis2JkYrJSJiRyUiY0dGJ1tbW1tbW1tbW11bW21GKVxbW1tbW1tbW1xbW20hIiNbW1tcW1tcW1tbW1ttIiIlXVtbW1tbW1tbW1tbbUYpRihGKCwoRidGKEYrRihGLCMhIiJGKkYl