Questions (Problem images provided below): Intro to Matlab Questions 5.2, 5.3, 5.7 coding and hand written appreciated.

5.2: Show the eienvalues of the following matrix are 3, -1, 1. [1 1 2; 4 1 5; 0 0 1]

5.3: Find the Eigen values of the following matrix by solving for the roots of the characteristic equation. [10 0 0, -1 -3 -7, 0 2 6]

5.7: Apply the power method to find the largest eigenvalue of the matrix from Problem 5.2 starting with the vector [1 1 1]^T.

Eigenvalues and Eigenve Chapter 5 186 5.8 PROBLEMS Problems to be solved by hand Solve the following problems by hand. When needed, use a calculator; or write a MATLAB script fi carry out the calculations. If using MATLAB, do not use buil-in functions for operations with matrices, 5.1 Show that the eigenvalues of the n x n identity matrix are the number 1 repeated n times. 5.2 Show that the eigenvalues of the following matrix are 3,-1, 1. 1 1 2 4 1 5 001 5.3 Find the eigenvalues of the following matrix by solving for the roots of the characteristic equation. 10 0 0 1 -3-7 5.4 The moment of inertia I, 1,, and the product of inertint 0 mm