Question

Classify the solution of the linear system, where the options are:

a. Sink node.

b. Source node.

c. Saddle node.

d. Sink spiral.

e. Source spiral.

f. Center.

g. None of the options displayed.

Answer 1

The options for classifying the solution of a linear system are: sink node, source node, saddle node, sink spiral, source spiral, center, or none of the options displayed. The classification is based on the eigenvalues and eigenvectors of the system's coefficient matrix.

Step-by-step explanation:

The given options to classify the solution of a linear system are:

1. Sink node - a solution that is vertically downward in the coordinate system.
2. Source node - a solution that is vertically upward in the coordinate system.
3. Saddle node - a solution that is horizontally to the right side of the coordinate system.
4. Sink spiral - a solution that is horizontally to the left side of the coordinate system.
5. Source spiral - a solution that forms a spiral shape with positive slope.
6. Center - a solution that forms a spiral shape with negative slope.
7. None of the options displayed - if the solution does not fit any of the given options.

To classify the solution of a linear system, you need to analyze the eigenvalues and eigenvectors of the system's coefficient matrix. Different combinations of eigenvalues and eigenvectors correspond to different classifications listed above.