Linear Algebra Quiz _ Week 5 - Diagonalization-Dyn. Systems

Which of the following is a necessary condition for a matrix to be diagonalizable?

• The matrix must be square.

• The matrix must have real eigenvalues.

• The matrix must have distinct eigenvalues.

• The matrix must have orthogonal columns.

What is the relationship between the eigenvectors of a matrix and its diagonalization?

• The eigenvectors form a diagonal matrix.

• The eigenvectors are the columns of the matrix used to diagonalize.

• The eigenvectors determine the eigenvalues.

• The eigenvectors are not involved in diagonalization.

If a matrix is not diagonalizable, what could be the possible cause?

• The matrix has complex eigenvalues.

• The matrix does not have enough linearly independent eigenvectors.

• The matrix has repeated eigenvalues.

• The matrix is symmetric.

• When all eigenvectors are linearly independent.

• When the matrix is square.

• When the eigenvalue is positive.

• The state of the system at any given time.

• The transition rule between states.

• The initial condition of the system.

• The solution of the system.

• Autonomous system

• Linear discrete-dynamic system

• Non-linear dynamic system

• Linear continuous-dynamic system

The general solution to a linear discrete-dynamic system involves what kind of expression?

• Exponential growth.

• Exponential decay.

• Oscillatory behavior.

• Steady state.