Homework Answers
![x = 2x + y y = Zr-5y writing it in matrix form. Let X= [3] 2X1 x = AX, where, Az ( i< (3]- [3 ][ ] 21 -5 - 2x2 Caracteristic](http://img.homeworklib.com/questions/0ade6dc0-108e-11eb-8beb-77c13eddafaa.png?x-oss-process=image/resize,w_560)
![=> X = çe 8 by] + zesti writing it in matrix form X = { }} = (-6, e-bt + C e 8c, ett + chelt 3t x =[%] = [. с 2. [ este C2 3t](http://img.homeworklib.com/questions/0b68c9e0-108e-11eb-afaa-3d702a92303d.png?x-oss-process=image/resize,w_560)
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6-Find the general solution of the following system. Write the solution in matrix form. (7 Points)...
Question Three: (7 marks) (a) Find the general solution of the following homogeneous equation. (b) Apply the method of Undetermined Coefficients to write ONLY the form of the particular solution of t...
Question Three: (7 marks) (a) Find the general solution of the following homogeneous equation. (b) Apply the method of Undetermined Coefficients to write ONLY the form of the particular solution of the following nonhomogeneous equation "-2y+5y 24re* cos(2x).
Question Three: (7 marks) (a) Find the general solution of the following homogeneous equation. (b) Apply the method of Undetermined Coefficients to write ONLY the form of the particular solution of the following nonhomogeneous equation "-2y+5y 24re* cos(2x).
Given the following system of linear equations 1. 2xi + 4x2 + 8 x3 + x. +2x,3 a) Write the augmented matrix that represents the system b) Find a reduced row echelon form (RREF) matrix that is row...
Given the following system of linear equations 1. 2xi + 4x2 + 8 x3 + x. +2x,3 a) Write the augmented matrix that represents the system b) Find a reduced row echelon form (RREF) matrix that is row equivalent to the augmented matrix c) Find the general solution of the system d) Write the homogeneous system of equations associated with the above (nonhomogeneous) system and find its general solution.
Given the following system of linear equations 1. 2xi + 4x2...
2. (12 points) Write the ODEs as a 2 x 2 system and then find the general solution using the eige...
2. (12 points) Write the ODEs as a 2 x 2 system and then find the general solution using the eigenvalues and eigenvectors of the constant (0) 9. matrix that appears in your system. Find the solution if the initial values are x(0)(0)-y(0)0 and
2. (12 points) Write the ODEs as a 2 x 2 system and then find the general solution using the eigenvalues and eigenvectors of the constant (0) 9. matrix that appears in your system. Find the...
3. Write the following systems of linear equations using augmented matrix form a. 6x+7y= -9 X-y=...
3. Write the following systems of linear equations using augmented matrix form a. 6x+7y= -9 X-y= 5 b. 2x-5y= 4 4x+3y= 5 C. x+y+z= 4 2x-y-z= 2 -x+2y+3z= 5 4. Solve the following Systems of linear equations using Cramer's Rule a. 6x-3y=-3 8x-4y= -4 b. 2x-5y= -4 4x+3y= 5 c. 2x-3y+z= 5 X+2y+z= -3 x-3y+2z= 1
5. Given the system of equations (92 – X – 5y + 7 = 0 x...
5. Given the system of equations (92 – X – 5y + 7 = 0 x – y + 32 – 1 = 0 2x + y = 5 = a. Write the system in the matrix form AX b. [1 points] b. Write out the augmented matrix for this system and calculate its row-reduced echelon form. [2 points] c. Write out the complete set of solutions. [2 points]
Exercise 2.5.152: Apply the method of undetermined coefficients to find the general solution to the following...
Exercise 2.5.152: Apply the method of undetermined coefficients
to find the general solution to the following DEs. Determine the
form and coefficients of yp
Exercise 2.5.152: Apply the method of undetermined coefficients to find the general solution to the following DEs. Determine the form and coefficients of yp a) y" – 2y' = 8x + 5e3x b) y'"' + y" – 2y' = 2x + e2x c) y'' + 6y' + 13y = cos x d) y'" + y" –...
2,3, 6, 7 1. Without matrices, solve the following system using the Gaussian elimination method +...
2,3, 6, 7
1. Without matrices, solve the following system using the Gaussian elimination method + 1 + HP 6x - Sy- -2 2. Consider the following linear system of equation 3x 2 Sy- (a) Write the augmented matrix for this linear system (b) Use row operations to transform the augmented matrix into row.echelon form (label all steps) (c) Use back substitution to solve the linear system. (find x and y) x + 2y 2x = 5 3. Consider the...
(6 points) Evaluate the following system using the augmented matrix method. When performing row reduction, be...
(6 points) Evaluate the following system using the augmented matrix method. When performing row reduction, be sure to indicate your row operations. x 2x -x + 2y + 5y + 4y – + – 2= z = 2z = -3 1 3 (12 points) Evaluate the following system using Gauss-Jordan elimination. When per- forming row reduction, be sure to indicate your row operations. 2x x -x (a) – + + y + z = y + 2z = 3y +...
Find the general solution of the following differential equation: (1) ?′′ + 5?′ + 6? =...
Find the general solution of the following differential
equation: (1) ?′′ + 5?′ + 6? = 2????*?^? (2) ?′′ + 2?′ + ? = ? +
?e^(-t).
(please solve Question No.7 only)
7. (30 points) Find the general solution of the following differential equation: (1) y" + 5y' + 6y = 2etsint (2) y" + 2y + y=t+te-t 8. (10 points) Use the method of variation of parameters to find a particular solution of y" + y = 1/sin (t),...
(1 point) Find the general solution of the following system. Give the answer in real form...
(1 point) Find the general solution of the following system. Give the answer in real form (no complex numbers or complex exponentials) t)(t)5y(t) 2(t)-G | (2/5cost-1/5sint) y(t)-c| | cost + sint
Question Three: (7 marks) (a) Find the general solution of the following homogeneous equation. (b) Apply the method of Undetermined Coefficients to write ONLY the form of the particular solution of the following nonhomogeneous equation "-2y+5y 24re* cos(2x).
Question Three: (7 marks) (a) Find the general solution of the following homogeneous equation. (b) Apply the method of Undetermined Coefficients to write ONLY the form of the particular solution of the following nonhomogeneous equation "-2y+5y 24re* cos(2x).
Given the following system of linear equations 1. 2xi + 4x2 + 8 x3 + x. +2x,3 a) Write the augmented matrix that represents the system b) Find a reduced row echelon form (RREF) matrix that is row equivalent to the augmented matrix c) Find the general solution of the system d) Write the homogeneous system of equations associated with the above (nonhomogeneous) system and find its general solution.
Given the following system of linear equations 1. 2xi + 4x2...
2. (12 points) Write the ODEs as a 2 x 2 system and then find the general solution using the eigenvalues and eigenvectors of the constant (0) 9. matrix that appears in your system. Find the solution if the initial values are x(0)(0)-y(0)0 and
2. (12 points) Write the ODEs as a 2 x 2 system and then find the general solution using the eigenvalues and eigenvectors of the constant (0) 9. matrix that appears in your system. Find the...
3. Write the following systems of linear equations using augmented matrix form a. 6x+7y= -9 X-y= 5 b. 2x-5y= 4 4x+3y= 5 C. x+y+z= 4 2x-y-z= 2 -x+2y+3z= 5 4. Solve the following Systems of linear equations using Cramer's Rule a. 6x-3y=-3 8x-4y= -4 b. 2x-5y= -4 4x+3y= 5 c. 2x-3y+z= 5 X+2y+z= -3 x-3y+2z= 1
5. Given the system of equations (92 – X – 5y + 7 = 0 x – y + 32 – 1 = 0 2x + y = 5 = a. Write the system in the matrix form AX b. [1 points] b. Write out the augmented matrix for this system and calculate its row-reduced echelon form. [2 points] c. Write out the complete set of solutions. [2 points]
Exercise 2.5.152: Apply the method of undetermined coefficients
to find the general solution to the following DEs. Determine the
form and coefficients of yp
Exercise 2.5.152: Apply the method of undetermined coefficients to find the general solution to the following DEs. Determine the form and coefficients of yp a) y" – 2y' = 8x + 5e3x b) y'"' + y" – 2y' = 2x + e2x c) y'' + 6y' + 13y = cos x d) y'" + y" –...
2,3, 6, 7
1. Without matrices, solve the following system using the Gaussian elimination method + 1 + HP 6x - Sy- -2 2. Consider the following linear system of equation 3x 2 Sy- (a) Write the augmented matrix for this linear system (b) Use row operations to transform the augmented matrix into row.echelon form (label all steps) (c) Use back substitution to solve the linear system. (find x and y) x + 2y 2x = 5 3. Consider the...
(6 points) Evaluate the following system using the augmented matrix method. When performing row reduction, be sure to indicate your row operations. x 2x -x + 2y + 5y + 4y – + – 2= z = 2z = -3 1 3 (12 points) Evaluate the following system using Gauss-Jordan elimination. When per- forming row reduction, be sure to indicate your row operations. 2x x -x (a) – + + y + z = y + 2z = 3y +...
Find the general solution of the following differential
equation: (1) ?′′ + 5?′ + 6? = 2????*?^? (2) ?′′ + 2?′ + ? = ? +
?e^(-t).
(please solve Question No.7 only)
7. (30 points) Find the general solution of the following differential equation: (1) y" + 5y' + 6y = 2etsint (2) y" + 2y + y=t+te-t 8. (10 points) Use the method of variation of parameters to find a particular solution of y" + y = 1/sin (t),...
(1 point) Find the general solution of the following system. Give the answer in real form (no complex numbers or complex exponentials) t)(t)5y(t) 2(t)-G | (2/5cost-1/5sint) y(t)-c| | cost + sint
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