Enter the matrix A and the vector b in MATLAB:

A = [4 1 2 −3; −3 3 −1 4; −1 2 5 1; 5 4 3 −1] , b = [−16;20;−4;−10]

The exact solution to the system Ax = b is the vector x = (−1, 1, −2, 3)^T .

(a) Enter [L, U,P] = lu(A) to find the LU decomposition of the matrix P A (don’t forget that you will need P*b). Verify that P A = LU.

(b) Use the LU decomposition you found in part (a) to solve the system Ax = b. Call the computed solution x_lu.

(c) Enter the vector x and compare your solution x lu from part (b) with the exact solution x by computing norm(x_lu - x)

During a steady flow process, the change of energy with respect to time is zero. a)- true b)- false

The characteristic roots of a dynamic system are: 1.7920 1.8160 i, -1.7920 1.8160 i, -0.4160 what is the order of this system? what are the settling time and damping ratio of the system?

An engine, weighing 3000 n, is supported on a pedestal mount. it has been observed that the engine induces vibration into the surrounding area through its pedestal at the maximum operating speed. determine the stiffness of the dynamic vibration absorber spring in (n/m) that will reduce the vibration when mounted on the pedestal. the magnitude of the exciting force is 250 n, and the amplitude of motion of the auxiliary mass is to be limited to 2 mm note: in this question type-in right numbers, no decimals, no fractions, no unit. approximate to right number if needed