Exam 7: Systems of First-Order Linear Equations

Consider the first-order homogeneous system of linear differential equations If the system were equipped with the initial condition what is the particular solution of the system?

Consider the first-order homogeneous system of linear differential equations Which of these is the general solution of the system? Here, C₁ and C₂ are arbitrary real constants.

Consider the following system of linear equations: The system is inconsistent.

Consider the first-order homogeneous system of linear differential equations Which of these is an accurate description of the solution trajectories of the phase portrait for this system?

Consider the first-order homogeneous system of linear differential equations The eigenvalues and corresponding eigenvectors for this system are: Which of these is the general solution for this system?

Consider the first-order homogeneous system of linear differential equations Select all of the eigenvalue-eigenvector pairs from the following choices.

Consider these matrices: D = E = Compute

Consider this system of first-order differential equations: Transform this system into a second-order differential equation whose solution is X₂ .

Consider the first-order homogeneous system of linear differential equations What is the general solution of this system?

Consider the following system of linear equations: Reduce the augmented matrix of this system to echelon form.

Consider the first-order homogeneous system of linear differential equations ? Given a fundamental matrix (t) for the system, for what constant vector does

Consider the first-order nonhomogeneous initial value problem Which of these is the fundamental matrix (t) for this system?

Consider the first-order homogeneous system of linear differential equations Which of these is the fundamental matrix (t) for this system?

Into which of the following systems can this homogeneous third-order differential equation be transformed?

Express the following third-order nonhomogeneous differential equation as a matrix equation of the form

Consider the first-order nonhomogeneous initial value problem Given a fundamental matrix (t) for the system, what is the solution of this initial value problem?

Consider the following system of linear equations: Find a condition involving that ensures the system has infinitely many solutions.

Consider a system of homogeneous first-order linear differential equations of the form = Ax, where A is a 2 × 2 constant matrix. are solutions of this system, which of the following must also be solutions of this system? Select all that apply.

Consider the first-order nonhomogeneous initial value problem Write simplified formulas for the components of the solution vector

Consider the first-order homogeneous system of linear differential equations Which of these are eigenvalues for this system? Select all that apply.