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Homework Answers
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(b) Consider the initial value problem ܚܕ ܠ ܂...
Need this asap Thanks k 0 1 (c) Consider the matrix 0 k 2 -2 k...
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k 0 1 (c) Consider the matrix 0 k 2 -2 k 3 i. Compute the determinant. ii. For what value(s) of k does A- exist? iii. For what value(s) of k does the linear system Ai= have nontrivial solutions? iv. For what value(s) of k does A have zero as an eigenvalue? v. For any vector 5 € R", find the value(s) of k for which the linear system Až = b has a unique...
(a) Solve the initial value problem 2" +2r' + r = 8(t - 2), z(0)=1, 2'0)...
(a) Solve the initial value problem 2" +2r' + r = 8(t - 2), z(0)=1, 2'0) = 2 (b) Consider the initial value problem -2 -5 z(0) = 3 Find ö(t), writing your answer as a single vector. k 2 k 0 1] (c) Consider the matrix 0 -2 k 3 i. Compute the determinant. ii. For what value(s) of k does A exist? iii. For what value(s) of k does the linear system A7 = 7 have nontrivial solutions?...
0 1 (c) Consider the matrix0 2 -2 k 3 i. Compute the determinant. ii. For...
0 1 (c) Consider the matrix0 2 -2 k 3 i. Compute the determinant. ii. For what value(s) of k does A exist? iii. For what value(s) of k does the linear system A7 = 7 have nontrivial solutions? iv. For what value(s) of k does A have zero as an eigenvalue? v. For any vector be R*, find the value(s) of k for which the linear system A7 = b has a unique solution.
linear algebra kindly show full solutions for upvotes Question: Consider the linear system of differential equations...
linear algebra
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Question: Consider the linear system of differential equations Vi = 8yi ป = 541 1072 792 1. (2 marks) Find the eigenvalues of the coefficient matrix and corresponding eigenvectors 2. (2 marks) Solve the system 3.(2 marks) Find the solution that satisfies the initial value conditions yı(0) = -1, ya(0) = 3
Problem 1 Consider the matrix Problem 1 Consider the matriz a 2 5 3 11 08...
Problem 1 Consider the matrix Problem 1 Consider the matriz a 2 5 3 11 08 a Find the cofactors C11,C2,C3 of A. b Find the determinant of 1, det(A) [ 2 4 61 Problem 2 Consider the matriz A=008 | 2 5 3 a Use the ero's to put A in upper triangular form 5 Pinul the determinant of A. (A) by keeping track of the row operations in part a and the properties of determinant Problem 3 Consider...
1 point) Consider the initial value problem 0 -2 a. Find the eigenvalue λ, an eigenvector...
1 point) Consider the initial value problem 0 -2 a. Find the eigenvalue λ, an eigenvector UI, and a generalized eigenvector v2 for the coefficient matrix of this linear system. v2 = b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers. c. Solve the original initial value problem. n(t)- 2(t)
(1 point) Consider the initial value problem -51เซี. -4 มี(0) 0 -5 a Find the eigenvalue λ, an eigenvector ul and a gen...
(1 point) Consider the initial value problem -51เซี. -4 มี(0) 0 -5 a Find the eigenvalue λ, an eigenvector ul and a generalized eigenvector u2 for the coefficient matrix of this linear system -5 u2 = b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers c2 c. Solve the original initial value problem m(t) = 2(t)-
(1 point) Consider the initial value problem -51เซี. -4 มี(0)...
Q1, pease help asap, please write clearly. Thanks in advance. 1. Given the transfer function of...
Q1, pease help asap, please write clearly. Thanks in
advance.
1. Given the transfer function of the control system. (60%) G(s) S) 5s+13 R(s) +6s+13 Y (1) Sketch the state diagram in the form of signal flow graph. (2) Find the state equations. (3) Find the output equation. (4) Find the fundamental matrix 2(t). (5) Find the state-transition matrix D(t) (6) Find the state vector x(t) if the input r(t) 2 and y(0)= (0) = 0 .
1. Given the...
(1 point) Consider the initial value problem -2 j' = [ y, y(0) +3] 0 -2...
(1 point) Consider the initial value problem -2 j' = [ y, y(0) +3] 0 -2 a. Find the eigenvalue 1, an eigenvector 1, and a generalized eigenvector ū2 for the coefficient matrix of this linear system. = --1 V2 = b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers. g(t) = C1 + C2 c. Solve the original initial value problem. yı(t) = y2(t) ==
I know A-D. Please do E-G only. Thanks! [ 1 ] [ 0 ] = W,...
I know A-D. Please do E-G only. Thanks!
[ 1 ]
[ 0 ] = W, W_2 is found in part F
[ 1 ]
3. (Taken from Boyce & DiPrima) Consider the 3-dimensional system of linear equations Ti 11] X' = AX = 2 1 -1 x 1-3 2 4 (a) Show that the three eigenvalues of the coefficient matrix, A, are 1, = lyd = 2. This is an eigenvalue of multiplicity 3. (b) Show that all the...
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k 0 1 (c) Consider the matrix 0 k 2 -2 k 3 i. Compute the determinant. ii. For what value(s) of k does A- exist? iii. For what value(s) of k does the linear system Ai= have nontrivial solutions? iv. For what value(s) of k does A have zero as an eigenvalue? v. For any vector 5 € R", find the value(s) of k for which the linear system Až = b has a unique...
(a) Solve the initial value problem 2" +2r' + r = 8(t - 2), z(0)=1, 2'0) = 2 (b) Consider the initial value problem -2 -5 z(0) = 3 Find ö(t), writing your answer as a single vector. k 2 k 0 1] (c) Consider the matrix 0 -2 k 3 i. Compute the determinant. ii. For what value(s) of k does A exist? iii. For what value(s) of k does the linear system A7 = 7 have nontrivial solutions?...
0 1 (c) Consider the matrix0 2 -2 k 3 i. Compute the determinant. ii. For what value(s) of k does A exist? iii. For what value(s) of k does the linear system A7 = 7 have nontrivial solutions? iv. For what value(s) of k does A have zero as an eigenvalue? v. For any vector be R*, find the value(s) of k for which the linear system A7 = b has a unique solution.
linear algebra
kindly show full solutions for upvotes
Question: Consider the linear system of differential equations Vi = 8yi ป = 541 1072 792 1. (2 marks) Find the eigenvalues of the coefficient matrix and corresponding eigenvectors 2. (2 marks) Solve the system 3.(2 marks) Find the solution that satisfies the initial value conditions yı(0) = -1, ya(0) = 3
Problem 1 Consider the matrix Problem 1 Consider the matriz a 2 5 3 11 08 a Find the cofactors C11,C2,C3 of A. b Find the determinant of 1, det(A) [ 2 4 61 Problem 2 Consider the matriz A=008 | 2 5 3 a Use the ero's to put A in upper triangular form 5 Pinul the determinant of A. (A) by keeping track of the row operations in part a and the properties of determinant Problem 3 Consider...
1 point) Consider the initial value problem 0 -2 a. Find the eigenvalue λ, an eigenvector UI, and a generalized eigenvector v2 for the coefficient matrix of this linear system. v2 = b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers. c. Solve the original initial value problem. n(t)- 2(t)
(1 point) Consider the initial value problem -51เซี. -4 มี(0) 0 -5 a Find the eigenvalue λ, an eigenvector ul and a generalized eigenvector u2 for the coefficient matrix of this linear system -5 u2 = b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers c2 c. Solve the original initial value problem m(t) = 2(t)-
(1 point) Consider the initial value problem -51เซี. -4 มี(0)...
Q1, pease help asap, please write clearly. Thanks in
advance.
1. Given the transfer function of the control system. (60%) G(s) S) 5s+13 R(s) +6s+13 Y (1) Sketch the state diagram in the form of signal flow graph. (2) Find the state equations. (3) Find the output equation. (4) Find the fundamental matrix 2(t). (5) Find the state-transition matrix D(t) (6) Find the state vector x(t) if the input r(t) 2 and y(0)= (0) = 0 .
1. Given the...
(1 point) Consider the initial value problem -2 j' = [ y, y(0) +3] 0 -2 a. Find the eigenvalue 1, an eigenvector 1, and a generalized eigenvector ū2 for the coefficient matrix of this linear system. = --1 V2 = b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers. g(t) = C1 + C2 c. Solve the original initial value problem. yı(t) = y2(t) ==
I know A-D. Please do E-G only. Thanks!
[ 1 ]
[ 0 ] = W, W_2 is found in part F
[ 1 ]
3. (Taken from Boyce & DiPrima) Consider the 3-dimensional system of linear equations Ti 11] X' = AX = 2 1 -1 x 1-3 2 4 (a) Show that the three eigenvalues of the coefficient matrix, A, are 1, = lyd = 2. This is an eigenvalue of multiplicity 3. (b) Show that all the...
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