Eigenvectors and Eigenvalues
... solutions A – λI is not invertible IMT all false The set {xεRn: (A – λI)x= 0} is the nullspace of (A – λI)x= 0, A a subspace of Rn The set of all solutions is called the eigenspace of A corresponding to λ ...
... solutions A – λI is not invertible IMT all false The set {xεRn: (A – λI)x= 0} is the nullspace of (A – λI)x= 0, A a subspace of Rn The set of all solutions is called the eigenspace of A corresponding to λ ...
(a) If xi(t) denotes the horizontal displacement of mi from equilibrium
... 0 m2 x2 (t) (Consider a force directed to the left to be positive.) Notice that the mass-stiffness equation Mx = Kx is the matrix version of Hooke’s law F = kx, and K is positive definite. (b) Look for a solution of the form x = eiθt v for a constant vector v, and show that this reduces the problem ...
... 0 m2 x2 (t) (Consider a force directed to the left to be positive.) Notice that the mass-stiffness equation Mx = Kx is the matrix version of Hooke’s law F = kx, and K is positive definite. (b) Look for a solution of the form x = eiθt v for a constant vector v, and show that this reduces the problem ...
Exam 3
... Problem 2: (15 points) True/False. If the statement is always true, mark true. Otherwise, mark false. You do not need to show your work. (Any work will not be graded.) (a) There exists a real 2 × 2 matrix, A, with eigenvalues λ1 = 1, λ2 = i. (b) If λ = 2 is a repeated eigenvalue of multiplicity 2 fo ...
... Problem 2: (15 points) True/False. If the statement is always true, mark true. Otherwise, mark false. You do not need to show your work. (Any work will not be graded.) (a) There exists a real 2 × 2 matrix, A, with eigenvalues λ1 = 1, λ2 = i. (b) If λ = 2 is a repeated eigenvalue of multiplicity 2 fo ...
