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Math 254 Math 254 Lecture Notes Notes Lecture Notes (10 pts) Find the of the matrix...
(1 point) Find the eigenvalues of the matrix A . -19 6 0 0 -36 11...
(1 point) Find the eigenvalues of the matrix A . -19 6 0 0 -36 11 0 0 A= The eigenvalues are λ| < λ2 < λ3 < λ4, where has an eigenvector 12 has an eigenvector has an eigenvector 4 has an eigenvector Note: you may want to use a graphing calculator to estimate the roots of the polynomial which defines the eigenvalues
(1 point) Given that ū = and are eigenvectors of the matrix -12 24 determine the...
(1 point) Given that ū = and are eigenvectors of the matrix -12 24 determine the corresponding eigenvalues. 21 = -1 12 = 1 (1 point) Solve the system -6 1 dx dt х -6 -1 with the initial value 0 x(0) = -2 x(t) = (1 point) Calculate the eigenvalues of this matrix: [Note-- you'll probably want to use a calculator or computer to estimate the roots of the polynomial which defines the eigenvalues. You also may want to...
(1 point) Calculate the eigenvalues of this matrix: [Note-- you'll probably want to use a calculator...
(1 point) Calculate the eigenvalues of this matrix: [Note-- you'll probably want to use a calculator or computer to estimate the roots of the polynomial which defines the eigenvalues. You also may want to view a phase plane plot (right click to open in a new window).]] 46 A -4 38 -5 smaller eigenvalue associated eigenvector = larger eigenvalue associated, eigenvector (1 point) Consider the system of differential equations dr dt 3x + 0.5y, dy 2.5x + y. dt For...
(1 point) a. Find the most general real-valued solution to the linear system of differential equations...
(1 point) a. Find the most general real-valued solution to the linear system of differential equations x -8 -10 x. xi(t) = C1 + C2 x2(t) b. In the phase plane, this system is best described as a source / unstable node sink / stable node saddle center point / ellipses spiral source spiral sink none of these ОООООО (1 point) Calculate the eigenvalues of this matrix: [Note-- you'll probably want to use a calculator or computer to estimate the...
(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...
Section 6.1 Eigenvalues and Eigenvectors: Problem 10 Previous Problem Problem List Next Problem 4 and the...
Section 6.1 Eigenvalues and Eigenvectors: Problem 10 Previous Problem Problem List Next Problem 4 and the determinant is det(A) --- 45. Find the eigenvalues of A. (1 point) Suppose that the trace of a 2 x 2 matrix A is tr(A) smaller eigenvalue larger eigenvalue Note: You can earn partial credit on this problem Preview My Answers Submit Answers Section 6.1 Eigenvalues and Eigenvectors: Problem 8 Previous Problem Problem List Next Problem (1 point) Find the eigenvalues di < 12...
(1 point) Find the characteristic polynomial of the matrix 5 -5 A = 0 [ 5...
(1 point) Find the characteristic polynomial of the matrix 5 -5 A = 0 [ 5 -5 -2 5 0] 4. 0] p(x) = (1 point) Find the eigenvalues of the matrix [ 23 C = -9 1-9 -18 14 9 72 7 -36 : -31] The eigenvalues are (Enter your answers as a comma separated list. The list you enter should have repeated items if there are eigenvalues with multiplicity greater than one.) (1 point) Given that vi =...
(1 point) Find the eigenvalues , < 12 <13 and associated unit eigenvectors ul, 2, uz...
(1 point) Find the eigenvalues , < 12 <13 and associated unit eigenvectors ul, 2, uz of the symmetric matrix -2 -2 - 2 0 A= 4 -2 -4 0 The eigenvalue 11 -6 has associated unit eigenvector új 1 1 1 The eigenvalue 12 has associated unit eigenvector iz 0 -2 1 1 The eigenvalue 12 0 has associated unit eigenvector üg -2 1 1 The eigenvalue 3 = 4 has associated unit eigenvector ūg 0 -1 1 Note:...
(1 point) Consider the system of differential equations dx dt = -1.6x + 0.5y, dy dt...
(1 point) Consider the system of differential equations dx dt = -1.6x + 0.5y, dy dt = 2.5x – 3.6y. For this system, the smaller eigenvalue is -41/10 and the larger eigenvalue is -11/10 [Note-- you may want to view a phase plane plot (right click to open in a new window).] If y' Ay is a differential equation, how would the solution curves behave? All of the solutions curves would converge towards 0. (Stable node) All of the solution...
[-5 0 5 5 0 -5 0 0 0 0 -5 0 0 0-5 0 (1 point) 2 The matrix A- has two distinct eigenvalues λ1 < λ...
[-5 0 5 5 0 -5 0 0 0 0 -5 0 0 0-5 0 (1 point) 2 The matrix A- has two distinct eigenvalues λ1 < λ2. Find the eigenvalues and a basis for each eigenspace. whose eigenspace has a basis of , whose eigenspace has a basis of | [1,0,0,1] Note: You can earn partial credit on this problem Preview My Answers Submit Answers Your score was recorded. You have attempted this problem 9 times. You received a...
(1 point) Find the eigenvalues of the matrix A . -19 6 0 0 -36 11 0 0 A= The eigenvalues are λ| < λ2 < λ3 < λ4, where has an eigenvector 12 has an eigenvector has an eigenvector 4 has an eigenvector Note: you may want to use a graphing calculator to estimate the roots of the polynomial which defines the eigenvalues
(1 point) Given that ū = and are eigenvectors of the matrix -12 24 determine the corresponding eigenvalues. 21 = -1 12 = 1 (1 point) Solve the system -6 1 dx dt х -6 -1 with the initial value 0 x(0) = -2 x(t) = (1 point) Calculate the eigenvalues of this matrix: [Note-- you'll probably want to use a calculator or computer to estimate the roots of the polynomial which defines the eigenvalues. You also may want to...
(1 point) Calculate the eigenvalues of this matrix: [Note-- you'll probably want to use a calculator or computer to estimate the roots of the polynomial which defines the eigenvalues. You also may want to view a phase plane plot (right click to open in a new window).]] 46 A -4 38 -5 smaller eigenvalue associated eigenvector = larger eigenvalue associated, eigenvector (1 point) Consider the system of differential equations dr dt 3x + 0.5y, dy 2.5x + y. dt For...
(1 point) a. Find the most general real-valued solution to the linear system of differential equations x -8 -10 x. xi(t) = C1 + C2 x2(t) b. In the phase plane, this system is best described as a source / unstable node sink / stable node saddle center point / ellipses spiral source spiral sink none of these ОООООО (1 point) Calculate the eigenvalues of this matrix: [Note-- you'll probably want to use a calculator or computer to estimate the...
(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...
Section 6.1 Eigenvalues and Eigenvectors: Problem 10 Previous Problem Problem List Next Problem 4 and the determinant is det(A) --- 45. Find the eigenvalues of A. (1 point) Suppose that the trace of a 2 x 2 matrix A is tr(A) smaller eigenvalue larger eigenvalue Note: You can earn partial credit on this problem Preview My Answers Submit Answers Section 6.1 Eigenvalues and Eigenvectors: Problem 8 Previous Problem Problem List Next Problem (1 point) Find the eigenvalues di < 12...
(1 point) Find the characteristic polynomial of the matrix 5 -5 A = 0 [ 5 -5 -2 5 0] 4. 0] p(x) = (1 point) Find the eigenvalues of the matrix [ 23 C = -9 1-9 -18 14 9 72 7 -36 : -31] The eigenvalues are (Enter your answers as a comma separated list. The list you enter should have repeated items if there are eigenvalues with multiplicity greater than one.) (1 point) Given that vi =...
(1 point) Find the eigenvalues , < 12 <13 and associated unit eigenvectors ul, 2, uz of the symmetric matrix -2 -2 - 2 0 A= 4 -2 -4 0 The eigenvalue 11 -6 has associated unit eigenvector új 1 1 1 The eigenvalue 12 has associated unit eigenvector iz 0 -2 1 1 The eigenvalue 12 0 has associated unit eigenvector üg -2 1 1 The eigenvalue 3 = 4 has associated unit eigenvector ūg 0 -1 1 Note:...
(1 point) Consider the system of differential equations dx dt = -1.6x + 0.5y, dy dt = 2.5x – 3.6y. For this system, the smaller eigenvalue is -41/10 and the larger eigenvalue is -11/10 [Note-- you may want to view a phase plane plot (right click to open in a new window).] If y' Ay is a differential equation, how would the solution curves behave? All of the solutions curves would converge towards 0. (Stable node) All of the solution...
[-5 0 5 5 0 -5 0 0 0 0 -5 0 0 0-5 0 (1 point) 2 The matrix A- has two distinct eigenvalues λ1 < λ2. Find the eigenvalues and a basis for each eigenspace. whose eigenspace has a basis of , whose eigenspace has a basis of | [1,0,0,1] Note: You can earn partial credit on this problem Preview My Answers Submit Answers Your score was recorded. You have attempted this problem 9 times. You received a...
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