Mr Ng's MA1513 Championship - Round 6

For an equilibrium point to be asymptotically stable, _____.

• all eigenvalues of the coefficient matrix must have negative real parts

• all eigenvalues of the coefficient matrix must have positive real parts

• at least one eigenvalue of the coefficient matrix must have a negative real part

• at least one eigenvalue of the coefficient matrix must have a positive real part

A saddle point is _____.

• always asymptotically stable

• always neutrally stable

• always unstable

• sometimes unstable

What type of equilibrium point is always neutrally stable?

• node

• saddle point

• spiral point

• center

In the context of complex eigenvalues, what does the term "conjugate pair" refer to?

• Two identical eigenvalues

• Two eigenvalues with opposite signs

• Two eigenvalues with the same real part and opposite imaginary parts

• Two eigenvalues with the same imaginary part and opposite real parts

Generalized eigenvectors are used when the matrix _____.

• is not square

• is not invertible

• has complex eigenvalues

• does not have enough linearly independent eigenvectors