a) Find the eigenvalues and the eigenvectors of the 2x2 matrix: [4 2] [3 -1] b)...
a) Find the eigenvalues and the eigenvectors of the 2x2 matrix:
[4 2]
[3 -1]
b) Solve the initial value problem:
dx/dt = 4x + 2y
dy/dt = 3x - y
with x(0) = 0, y(0) = 7
Homework Answers
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we first find eigenvalues and
eigenvectors of A then we find solution x(t).then we apply initial
condition to find constants.
Add Answer to:
a) Find the eigenvalues and the eigenvectors of the 2x2
matrix:
[4 2]
[3 -1]
b)...
($ ?) 4 2. (a) Find the eigenvalues and eigenvectors of the matrix 3 Hence or...
($ ?) 4 2. (a) Find the eigenvalues and eigenvectors of the matrix 3 Hence or otherwise find the general solution of the system = 4x + 2y = 3x - y 195 marks 5. (a) Give a precise definition of Laplace transform of a function f(t). Use your definition to determine the Laplace transform of 3. Osts 2 6-t, 2 <t f(t) = [20 marks] (b) A logistic initial value problem is given by dP dt kP(M-P), P(0) -...
(1 point) -1 -4 a. Given that V1 [ 2] and U2 --10 are eigenvectors of...
(1 point) -1 -4 a. Given that V1 [ 2] and U2 --10 are eigenvectors of the matrix _2] determine the corresponding eigenvalues. 4 11 = 12 = = -4x b. Find the solution to the linear system of differential equations x' y' satisfying the initial conditions x(0) = -3 and y(0) = 4. 4x – 2y x(t) = y(t) =
(1 point) a. Find the eigenvalues and eigenvectors of the matrix of the matrik (_&_7] 1...
(1 point) a. Find the eigenvalues and eigenvectors of the matrix of the matrik (_&_7] 1 2 1-6 3 -7] 11 = -4 ,u = , and 12 = -1 , 02 = → b. Solve the system of differential equations x X1(0) = [ 2 | -6 31+ -7 the initial conditions | x2(0) xi(t) = x2(t) =
Let A be a 2x2 matrix with eigenvalues 4 and and corresponding eigenvectors V, = and...
Let A be a 2x2 matrix with eigenvalues 4 and and corresponding eigenvectors V, = and v2 Let} be a solution of the difference equation X: 1 -AX. Xo' - a Computex, = Ax (Hint: You do not need to know itselt b. Find a formula for x, involving k and the eigenvectors V, and v2 a x Ax=(Type an integer or simplified fraction for each matrix element) b. xxv.v2 (Type expressions using k as the variable.)
MTH 295 Homework set # 7 The following problems will be fully graded with the possibility of earn...
MTH 295 Homework set # 7 The following problems will be fully graded with the possibility of earning partial credit. To receive any credit, you must show a sufficient amount of work when applicable. If you use additional paper to show your work, insert the additional work sheets between the test pages. DO NOT staple. Sloppy, haphazard work will not receive credit. Give the answers in the spaces provided, and the work on separate sheets of paper. Consider the following...
Problem 8. (15 points) Find eigenvalues and eigenvectors of the follwing matrix 3 -2 0 A= -1 3-2 0 -1 3 Problem 8. (15 points) Find eigenvalues and eigenvectors of the follwing matrix 3 -2 0...
Problem 8. (15 points) Find eigenvalues and eigenvectors of the follwing matrix 3 -2 0 A= -1 3-2 0 -1 3
Problem 8. (15 points) Find eigenvalues and eigenvectors of the follwing matrix 3 -2 0 A= -1 3-2 0 -1 3
Find the eigenvalues and associated eigenvectors of the matrix Q2: Find the eigenvalues and associated eigenvectors...
Find
the eigenvalues and associated eigenvectors of the matrix
Q2: Find the eigenvalues and associated eigenvectors of the matrix 7 0 - 3 A = - 9 2 3 18 0 - 8
Slove 2nd problem plz (1) Find the eigenvalues and corresponding eigenvectors of [o1 0 0 0...
Slove 2nd problem plz
(1) Find the eigenvalues and corresponding eigenvectors of [o1 0 0 0 1 2 1 -2 HINT: Note that 13 + 2/2 - 1 - 2 can be regrouped as 1(12 - 1)+2(12-1). Then factor out the common (12 - 1). (2) Solve the equation Y" + 2y' - - 2y = 0) using the method of converting to a linear system of first-order ODE's. Show that the coefficient matrix is the 3 x 3 matrix...
Problem 5. (1 point) Consider the linear system a. Find the eigenvalues and eigenvectors for the...
Problem 5. (1 point) Consider the linear system a. Find the eigenvalues and eigenvectors for the coefficient matrix. 1 = . and 12 = V2 = b. Find the real-valued solution to the initial value problem = -3y - 2y, 5y + 3y2 (0) = -11, y (0) = 15. Usef as the independent variable in your answers. y (t) = (1) =
Problem # 1: (70 points) Solve the following problems (a) and (b) using Laplace Transform: a) (7 ...
Problem # 1: (70 points) Solve the following problems (a) and (b) using Laplace Transform: a) (7 points) y(0)-y'(0)-0 y"(0)-1 b) (dX/d't) + 3 (dy/dt) + 3y-0 (7 points) (d'x/d't) +3y-te' x(0) = 0 x'(0) = 2 y(0) = 0 c) An nxn matrix A is said to be skew-symmetric if AT--A. If A is a 5x5 skew-symmetric matrix, show that 9detA)-0 (4 Points) d) Suppose A is a 5x5 matrix for which (detA) =-7, what is the value of...
($ ?) 4 2. (a) Find the eigenvalues and eigenvectors of the matrix 3 Hence or otherwise find the general solution of the system = 4x + 2y = 3x - y 195 marks 5. (a) Give a precise definition of Laplace transform of a function f(t). Use your definition to determine the Laplace transform of 3. Osts 2 6-t, 2 <t f(t) = [20 marks] (b) A logistic initial value problem is given by dP dt kP(M-P), P(0) -...
(1 point) -1 -4 a. Given that V1 [ 2] and U2 --10 are eigenvectors of the matrix _2] determine the corresponding eigenvalues. 4 11 = 12 = = -4x b. Find the solution to the linear system of differential equations x' y' satisfying the initial conditions x(0) = -3 and y(0) = 4. 4x – 2y x(t) = y(t) =
(1 point) a. Find the eigenvalues and eigenvectors of the matrix of the matrik (_&_7] 1 2 1-6 3 -7] 11 = -4 ,u = , and 12 = -1 , 02 = → b. Solve the system of differential equations x X1(0) = [ 2 | -6 31+ -7 the initial conditions | x2(0) xi(t) = x2(t) =
Let A be a 2x2 matrix with eigenvalues 4 and and corresponding eigenvectors V, = and v2 Let} be a solution of the difference equation X: 1 -AX. Xo' - a Computex, = Ax (Hint: You do not need to know itselt b. Find a formula for x, involving k and the eigenvectors V, and v2 a x Ax=(Type an integer or simplified fraction for each matrix element) b. xxv.v2 (Type expressions using k as the variable.)
MTH 295 Homework set # 7 The following problems will be fully graded with the possibility of earning partial credit. To receive any credit, you must show a sufficient amount of work when applicable. If you use additional paper to show your work, insert the additional work sheets between the test pages. DO NOT staple. Sloppy, haphazard work will not receive credit. Give the answers in the spaces provided, and the work on separate sheets of paper. Consider the following...
Problem 8. (15 points) Find eigenvalues and eigenvectors of the follwing matrix 3 -2 0 A= -1 3-2 0 -1 3
Problem 8. (15 points) Find eigenvalues and eigenvectors of the follwing matrix 3 -2 0 A= -1 3-2 0 -1 3
Find
the eigenvalues and associated eigenvectors of the matrix
Q2: Find the eigenvalues and associated eigenvectors of the matrix 7 0 - 3 A = - 9 2 3 18 0 - 8
Slove 2nd problem plz
(1) Find the eigenvalues and corresponding eigenvectors of [o1 0 0 0 1 2 1 -2 HINT: Note that 13 + 2/2 - 1 - 2 can be regrouped as 1(12 - 1)+2(12-1). Then factor out the common (12 - 1). (2) Solve the equation Y" + 2y' - - 2y = 0) using the method of converting to a linear system of first-order ODE's. Show that the coefficient matrix is the 3 x 3 matrix...
Problem 5. (1 point) Consider the linear system a. Find the eigenvalues and eigenvectors for the coefficient matrix. 1 = . and 12 = V2 = b. Find the real-valued solution to the initial value problem = -3y - 2y, 5y + 3y2 (0) = -11, y (0) = 15. Usef as the independent variable in your answers. y (t) = (1) =
Problem # 1: (70 points) Solve the following problems (a) and (b) using Laplace Transform: a) (7 points) y(0)-y'(0)-0 y"(0)-1 b) (dX/d't) + 3 (dy/dt) + 3y-0 (7 points) (d'x/d't) +3y-te' x(0) = 0 x'(0) = 2 y(0) = 0 c) An nxn matrix A is said to be skew-symmetric if AT--A. If A is a 5x5 skew-symmetric matrix, show that 9detA)-0 (4 Points) d) Suppose A is a 5x5 matrix for which (detA) =-7, what is the value of...
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