1 1 1 0 -5 0 -77 0 2. 0 2 2. Let A be a 4 x 5 matrix whose reduced row echelon form is R 0 0 0 3 LO 0 0 0 0 For parts (b) and (c), write the solution in parametric vector form. (a) (2 points) Is the equation Ax b consistent for all b in R4? Why or why not? (b) (4 points) Solve the equation Ax = 0. 4 -3 -3 (c) (3...
can you solve this problem please? 8. Determine the appropriate form of the particular solution for the following non-homogeneous linear differential equation with constant coefficients. * (8 Points) +9y" = 5 + e* (x – 3) + 4sin (3x). y (4) A + B sin(3x) + Cxsin (3x) + Det + Exer none of these A + Bxe-3x + Cxe3x + Det + Exet Ax2 + Bxe-3x + Cxe3x + Det + Exer Ax + B + C sin(3x) +...
Please solve all three. Thank you very much 5. (a) Let a be a constant (we can write “a ER” to mean “a is a real number”). Verify that y(x) = ci cos(ax) + C2 sin(ax) is a solution for y" = -a’y, where C1,C2 ER. (b) Consider the hyperbolic trigonometric functions defined by cosh(x) = et tex 2 ex – e- sinh(x) = * d Show that I cosh(x) = sinh(x) and sinh(x) = cosh(x). (e) Verify that y(x)...
Why c part is not yp= At^2cost +Bt^2sint WORK Question 1 (6+0+8+5-25 pts) a)Find the general solution of (Hint: 6 +3163 19r2 +3 10 (+1)-2+5).) (b) Find the form of a particular solution of (In other words, find the form of onc solution of the equation. Do not compute the coefficients.) dr ) Find the form of a particular solution of (Do not compute the coefficients.) CoS tt WORK Question 1 (6+0+8+5-25 pts) a)Find the general solution of (Hint: 6...
conic section Now consider the conic represented by the equation xyy-22x +2/2y-0. For this equation, it is more difficult to wrte t in the form -h. 1 because of the xyterm. When a conic with equaticon difficult to write it in the formk - 1 because of the xy term. When a conic with equation ax' + bxy + cy'+dx ey+-0 is rotated about an angle 6, where cot 20-converting from basis B: # {( 1, 0), (0, 1)) to...
Let a >0 Solve the following Laplace's equation in the disk: with the boundary conditions Assume that is a given periodic function with satisfying f (0) = f (2π) and Moreover, u(r,0 is bounded for r s a Which of the following is the (general) solution Select one: A. where for B. where )cos(n)de and for C. where and 2m for n- 1,2,3, D. where Co E R f(0) cos(n0)de and for Let a >0 Solve the following Laplace's equation...
1. (40pts) Let 8 >0 and hn: (8,2 - 8] -R be given by cos(n) hn (x) 72 Use Dirichlet's Test to show that the series hn converges uniformly on (8,27 - 8). That is, please solve the following problems: la. (10 pts) Let 9n (x) = . * € (8,27 - 8). Show that In - g uniformly, where g(x) = 0, for all 2 € (5,2 - 8) and 9n+1 () S (x). for all n e N...
y = 3x0+ QUESTION 2 Solve the given differential equation. (The form of yp is given D2y + 25y = -5 sin 5x (Let y p = Ax sin 5x + Bx cos 5x.) sin 5x + c2 cos 5x + x sin 5x - 1 x cos 5x Oo oo cos 5x + = x cos 5x y = C1 sin 5x + C2 cos 5x + 5x sin 5x y = C1 sin 5x + C2 cos 5x...
7. (20 points) Let 0-1 5 3 A -2 34 2 -3-5 (a) ( 15 points) Solve the linear system Ax = b by Gaussian elimination and express the general solution in vector form. (b) (5 points) Write down the corresponding homogenous system Ax-0 explicitly and determine all non-trivial solutions from (a) without resolving the system 7. (20 points) Let 0-1 5 3 A -2 34 2 -3-5 (a) ( 15 points) Solve the linear system Ax = b by...
Problem 1 Let A= 3 2 13 1 5 7 11 8 -3 9 10 -6 -4 12 8 a) [4 pts) Find a basis for N(A) in rational format. b) (3 pts) Find a particular solution to the matrix equation A*x= 5 -2 14 c) [3 pts] Use your answers in a), b) and the Superposition Principle to express the general solution in vector form to the matrix equation in b).