

16.) Use Cramer's Rule to solve for y: 2x - 3y + 4z = 1 + 6z=0 3x - 2y = 5 .
(10 points) For the differential equation y(6) - 2y (5) – 3y(4) + 2y(3) + 10y" – 8y = 0. Find the fundamental solution set to the DE if the characteristic equation in factored form is given by (r – 2) (r2 + 2r + 2) (r - 1) (r + 1) = 0
Question 12 Consider the following system of linear equations (x-y +z = -2 x – 3y - 2 = -1 3x +2y = -8 Which of the following method can be used to solve the above system? a) Gaussian climination b) Cramer's Rule c) Inverse Matrix d) All of the mentioned Your answer 0 del Bad Ps hp
Solve using Cramer's Rule X – 2y +z=7 2x +y – z=0 3x + 2y – 2z = -2 O (1,-2,0) O (2,-1,3) O (1,-1,1) No Solution
5. For the system, 4x + y + 2z = 1 2x + 3y + 4z = -5 x – y +3z = 3 Find the rank of the coefficient matrix by calculating the determinant. Use Cramer's theorem to find the solution of this system. (10 points) 6. Find the inverse of the following matrix using Gauss-Jordan method. Verify your result by computing the inverse using the method of determinants. (10 points) 1 2 4 2 4 2 1] 1...
(10 pts) Solve the following system using either Cramer's Rule or matrices (3x - 2y + 5z = -5 x – y + 3z = -4 4x + y + z = 5
1254 6B use Cramer's rule to solve linear system [ 3x+2y+43 = 17... (1) 2x+4y-32=8 (2) 44. By+22=-1 (3)
Consider the initial value problem y" +3y' +2y = (t-1)+r(t), y(0) = y(0) = 0, where 8(t-1) is Dirac's delta function and S4 if 0<t<1 r(t) 8 if t > 1 (a) Represent r(t) using unit step functions. (b) Find the Laplace Transform of 8(t-1)+r(t). (c) Solve the above initial value problem. {
3. (20 p.) Let 2x-2y + 6z = 18 , 3y =-6x + 15 and -9z + x +2y-7-0. Solve this linear equation system for variable y by using Cramer rule.
5. (11 points) Solve the following initial value problem, y" + 3y + 2y = g(t); y(0) = 0, 7(0) = 1/2 where g(t) = 38(t - 1) + uz(t) Type here to search