Finally, to demonstrate that your team understands how this process works, your team should create a small program that does the following: a. your program should start with a statement in comments at the top: "as a team, we have gone through all required sections of the tutorial, and each team member understands the material." b. creates 4 matrices, a, b, c, and d, of size 3x4,4x2, 2x3, and 3x1. you can use randomized or hardcode values for the entries. output each of these matrices. c. computes the product e = abc and outputs the resulting matrix. (note: this is matrix multiplication not simple elementwise multiplication.) d. prints the transpose of e. e. solves the linear system ex=d for x (this is the solve command).

Tom is having a problem with his washing machine. he notices that the machine vibrates violently at a frequency of 1500 rpm due to an unknown rotating unbalance. the machine is mounted on 4 springs each having a stiffness of 10 kn/m. tom wishes to add an undamped vibration absorber attached by a spring under the machine the machine working frequency ranges between 800 rpm to 2000 rpm and its total mass while loaded is assumed to be 80 kg a) what should be the mass of the absorber added to the machine so that the natural frequency falls outside the working range? b) after a first trial of an absorber using a mass of 35 kg, the amplitude of the oscillation was found to be 10 cm. what is the value of the rotating unbalance? c) using me-3.5 kg. m, find the optimal absorber (by minimizing its mass). what would be the amplitude of the oscillation of the absorber?