Homework Answers
Add Answer to:
Solving 1. Let -Ar, A constant, with real and distinct eigenvalues 3-1 0 2-2 3 A...
(1 point) Suppose that the matrix A has the following eigenvalues and eigenvectors: A1 = 4...
(1 point) Suppose that the matrix A has the following eigenvalues and eigenvectors: A1 = 4 with = and [2] [i] Az = 3 with Ū2 = Write the solution to the linear system r' = Ar in the following forms. A. In eigenvalue/eigenvector form: t (10) -- + C2 e e B. In fundamental matrix form: (39) - g(t). C. As two equations: (write "c1" and "c2" for C and C2) X(t) = g(t) = Note: if you are...
(1 point) The matrix 2 -1 0 A2-3 -1 has three distinct real eigenvalues if and only if
(1 point) The matrix 2 -1 0 A2-3 -1 has three distinct real eigenvalues if and only if
(1 point) The matrix 2 -1 0 A2-3 -1 has three distinct real eigenvalues if and only if
4. Consider the system y'- Ay(t), for t > 0, with A - 1 -2 (a) Show that the matrix A has eigenva...
4. Consider the system y'- Ay(t), for t > 0, with A - 1 -2 (a) Show that the matrix A has eigenvalues וג --1and Az--3 with corresponding eigenvectors u (1,1) and u2 (1,-1) (b) Sketch the trajectory of the solution having initial vector y(0) = ul. (c) Sketch the trajectory of the solution having initial vector y(0) -u2. (d) Sketch the trajectory of the solution having initial vector y(0)-u -u 1 U
4. Consider the system y'- Ay(t), for...
8. 20 pts.] Suppose that a 2 x2 matrix A has the following eigenvalues and eigenvectors:...
8. 20 pts.] Suppose that a 2 x2 matrix A has the following eigenvalues and eigenvectors: () 12, 1 r2=1, 2 2 (a) Classify the equilibrium 0 (node, saddle, spiral, center). Is it stable or unstable? (b) Sketch the trajectories of the system A , where a the phase plane below. (c) On the next page, sketch the graphs of r1 (t) and 2(t) versus t for the solution that satisfies the initial condition x1(0) = 1, x2(0) = 1...
# 2: Consider the real symmetric matrix A= 4 1 a) What are the eigenvalues and...
# 2: Consider the real symmetric matrix A= 4 1 a) What are the eigenvalues and eigenvectors. [Hint: Use wolframalpha.] b) What is the trace of A, what is the sum of the eigenvalues of A. What is a general theorem th c) The eigenvalues of A are real. What is a general theorem which assert conditions that t d) Check that the eigenvectors are real. What is a general theorem which asserts conditions th asserts equality? eigenvalues are real...
Suppose that the matrix A A has the following eigenvalues and eigenvectors: (1 point) Suppose that...
Suppose that the matrix A A has the following eigenvalues and
eigenvectors:
(1 point) Suppose that the matrix A has the following eigenvalues and eigenvectors: 2 = 2i with v1 = 2 - 5i and - 12 = -2i with v2 = (2+1) 2 + 5i Write the general real solution for the linear system r' = Ar, in the following forms: A. In eigenvalue/eigenvector form: 0 4 0 t MODE = C1 sin(2t) cos(2) 5 2 4 0 0...
Let A be the matrix To 1 0] A= -4 4 0 1-2 0 1 (a)...
Let A be the matrix To 1 0] A= -4 4 0 1-2 0 1 (a) Find the eigenvalues and eigenvectors of A. (b) Find the algebraic multiplicity an, and the geometric multiplicity, g, of each eigenvalue. (c) For one of the eigenvalues you should have gi < az. (If not, redo the preceding parts!) Find a generalized eigenvector for this eigenvalue. (d) Verify that the eigenvectors and generalized eigenvectors are all linearly independent. (e) Find a fundamental set of...
Show that any two eigenvectors of the symmetric matrix corresponding to distinct eigenvalues are orthogonal. -1...
Show that any two eigenvectors of the symmetric matrix corresponding to distinct eigenvalues are orthogonal. -1 0-1 0-1 0 -107 Find the characteristic polynomial of A. far - 41 - Find the eigenvalues of A. (Enter your answers from smallest to largest.) (11, 12, 13) = Find the general form for every eigenvector corresponding to 11. (Uses as your parameter.) X1 = Find the general form for every eigenvector corresponding to 12. (Use t as your parameter.) x2 = (0.t,0)...
linear algebra Show that any two eigenvectors of the symmetric matrix corresponding to distinct eigenvalues are...
linear algebra
Show that any two eigenvectors of the symmetric matrix corresponding to distinct eigenvalues are orthogonal -1 0-1 0-1 0 - 1 0 9 1 Find the characteristic polynomial of A. |x - Al- Find the eigenvalues of A. (Enter your answers from smallest to largest.) (21, 22, 23) Find the general form for every eigenvector corresponding to 21. (Uses as your parameter.) X1 - Find the general form for every elge vector corresponding to Az. (Uset as your...
(1 point) Consider the linear system -3 -2 - 5 3 a. Find the eigenvalues and...
(1 point) Consider the linear system -3 -2 - 5 3 a. Find the eigenvalues and eigenvectors for the coefficient matrix. 2 2 and 2 =i -3+i -3-i b. Find the real-valued solution to the initial value problem — Зул — 2у2, y1 (0)=-6, โบ,่ y2(0)= 15 5уд + Зуз, Use t as the independent variable in your answers. y1 (t) -6cos(t)+5sin(t) У2(t) 15cost+15sint
(1 point) Suppose that the matrix A has the following eigenvalues and eigenvectors: A1 = 4 with = and [2] [i] Az = 3 with Ū2 = Write the solution to the linear system r' = Ar in the following forms. A. In eigenvalue/eigenvector form: t (10) -- + C2 e e B. In fundamental matrix form: (39) - g(t). C. As two equations: (write "c1" and "c2" for C and C2) X(t) = g(t) = Note: if you are...
(1 point) The matrix 2 -1 0 A2-3 -1 has three distinct real eigenvalues if and only if
(1 point) The matrix 2 -1 0 A2-3 -1 has three distinct real eigenvalues if and only if
4. Consider the system y'- Ay(t), for t > 0, with A - 1 -2 (a) Show that the matrix A has eigenvalues וג --1and Az--3 with corresponding eigenvectors u (1,1) and u2 (1,-1) (b) Sketch the trajectory of the solution having initial vector y(0) = ul. (c) Sketch the trajectory of the solution having initial vector y(0) -u2. (d) Sketch the trajectory of the solution having initial vector y(0)-u -u 1 U
4. Consider the system y'- Ay(t), for...
8. 20 pts.] Suppose that a 2 x2 matrix A has the following eigenvalues and eigenvectors: () 12, 1 r2=1, 2 2 (a) Classify the equilibrium 0 (node, saddle, spiral, center). Is it stable or unstable? (b) Sketch the trajectories of the system A , where a the phase plane below. (c) On the next page, sketch the graphs of r1 (t) and 2(t) versus t for the solution that satisfies the initial condition x1(0) = 1, x2(0) = 1...
# 2: Consider the real symmetric matrix A= 4 1 a) What are the eigenvalues and eigenvectors. [Hint: Use wolframalpha.] b) What is the trace of A, what is the sum of the eigenvalues of A. What is a general theorem th c) The eigenvalues of A are real. What is a general theorem which assert conditions that t d) Check that the eigenvectors are real. What is a general theorem which asserts conditions th asserts equality? eigenvalues are real...
Suppose that the matrix A A has the following eigenvalues and
eigenvectors:
(1 point) Suppose that the matrix A has the following eigenvalues and eigenvectors: 2 = 2i with v1 = 2 - 5i and - 12 = -2i with v2 = (2+1) 2 + 5i Write the general real solution for the linear system r' = Ar, in the following forms: A. In eigenvalue/eigenvector form: 0 4 0 t MODE = C1 sin(2t) cos(2) 5 2 4 0 0...
Let A be the matrix To 1 0] A= -4 4 0 1-2 0 1 (a) Find the eigenvalues and eigenvectors of A. (b) Find the algebraic multiplicity an, and the geometric multiplicity, g, of each eigenvalue. (c) For one of the eigenvalues you should have gi < az. (If not, redo the preceding parts!) Find a generalized eigenvector for this eigenvalue. (d) Verify that the eigenvectors and generalized eigenvectors are all linearly independent. (e) Find a fundamental set of...
Show that any two eigenvectors of the symmetric matrix corresponding to distinct eigenvalues are orthogonal. -1 0-1 0-1 0 -107 Find the characteristic polynomial of A. far - 41 - Find the eigenvalues of A. (Enter your answers from smallest to largest.) (11, 12, 13) = Find the general form for every eigenvector corresponding to 11. (Uses as your parameter.) X1 = Find the general form for every eigenvector corresponding to 12. (Use t as your parameter.) x2 = (0.t,0)...
linear algebra
Show that any two eigenvectors of the symmetric matrix corresponding to distinct eigenvalues are orthogonal -1 0-1 0-1 0 - 1 0 9 1 Find the characteristic polynomial of A. |x - Al- Find the eigenvalues of A. (Enter your answers from smallest to largest.) (21, 22, 23) Find the general form for every eigenvector corresponding to 21. (Uses as your parameter.) X1 - Find the general form for every elge vector corresponding to Az. (Uset as your...
(1 point) Consider the linear system -3 -2 - 5 3 a. Find the eigenvalues and eigenvectors for the coefficient matrix. 2 2 and 2 =i -3+i -3-i b. Find the real-valued solution to the initial value problem — Зул — 2у2, y1 (0)=-6, โบ,่ y2(0)= 15 5уд + Зуз, Use t as the independent variable in your answers. y1 (t) -6cos(t)+5sin(t) У2(t) 15cost+15sint
Most questions answered within 3 hours.
-
Under the influence of its drive force, a snowmobile is moving
at a constant velocity along...
asked 1 hour ago -
Why do organizations decline? What steps can top
management take to halt, decline, and restore organizational...
asked 1 hour ago -
. Suppose a discrete random variable has probability
distribution
P(x) = .2 if x = 0...
asked 51 minutes ago -
What mechanisms Drive speciation??
(I.e. what was Dawins theory on the orgin of species, and how...
asked 2 hours ago -
The manager at a car assembly plant believes that the mean
assembly time for a car...
asked 3 hours ago -
Which of the following is true of electron capture?
A) It decreases the nuclide's mass number...
asked 5 hours ago -
Assuming an efficiency of 43.10%, calculate the actual yield of
magnesium nitrate formed from 114.9 g...
asked 5 hours ago -
The highly pathogenic bacterium Clostridium
perfringens causes gangrene, a disease that results in the
destruction of...
asked 7 hours ago -
In the context of situation analysis, which of the following is
a category for analysis in...
asked 7 hours ago -
In a study of the gas phase decomposition of sulfuryl chloride
at 600 K SO2Cl2(g)SO2(g) +...
asked 7 hours ago -
75 g of 2-propanol (C3H8O) and 25 g of pentane are mixed in a
200 mL...
asked 7 hours ago -
The 2800-turn coil in a dc motor has an area per turn of 1.1 ×
10-2...
asked 7 hours ago